Team for Advanced Flow Simulation and Modeling

Journal Publications

(Last update: Sep 23, 2023)

Journal Articles Indexed by the Web of Science (Researcher ID: F-6134-2012)

[278]

K. Takizawa and T.E. Tezduyar, “Space–time flow computation with boundary layer and contact representation: a 10-year history”, Computational Mechanics, published online, doi: 10.1007/s00466-023-02379-8 (2023), 10.1007/s00466-023-02379-8
@UNPUBLISHED{Takizawa23b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, TITLE = {Space--time flow computation with boundary layer and contact representation: a 10-year history}, YEAR = {2023}, DOI = {10.1007/s00466-023-02379-8}, NOTE = {\textit{Computational Mechanics}, published online, doi: 10.1007/s00466-023-02379-8} }

[277]

T.E. Tezduyar, K. Takizawa, and Y. Bazilevs, “Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces”, Mathematical Models and Methods in Applied Sciences, to appear (2023)
@UNPUBLISHED{Tezduyar23b, AUTHOR = {T. E.~Tezduyar and K.~Takizawa and Y.~Bazilevs}, TITLE = {Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces}, YEAR = {2023}, NOTE = {\textit{Mathematical Models and Methods in Applied Sciences}, to appear} }

[276]

T.E. Tezduyar and K. Takizawa, “Space–time computational flow analysis: Unconventional methods and first-ever solutions”, Computer Methods in Applied Mechanics and Engineering, published online, doi: 10.1016/j.cma.2023.116137 (2023), 10.1016/j.cma.2023.116137
@UNPUBLISHED{Tezduyar23a, AUTHOR = {T. E.~Tezduyar and K.~Takizawa}, TITLE = {Space--Time Computational Flow Analysis: {U}nconventional Methods and First-Ever Solutions}, YEAR = {2023}, DOI = {10.1016/j.cma.2023.116137}, NOTE = {\textit{Computer Methods in Applied Mechanics and Engineering}, published online, doi: 10.1016/j.cma.2023.116137} }

[275]

K. Takizawa, Y. Otoguro, and T.E. Tezduyar, “Variational multiscale method stabilization parameter calculated from the strain-rate tensor”, Mathematical Models and Methods in Applied Sciences, 33 (2023) 1661–1691, 10.1142/S0218202523500380
@ARTICLE{Takizawa23a, AUTHOR = {K.~Takizawa and Y.~Otoguro and T. E.~Tezduyar}, PAGES = {1661--1691}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {33}, TITLE = {Variational multiscale method stabilization parameter calculated from the strain-rate tensor}, YEAR = {2023}, DOI = {10.1142/S0218202523500380}, NUMBER = {8} }

[274]

Y. Bazilevs, K. Takizawa, T.E. Tezduyar, A. Korobenko, T. Kuraishi, and Y. Otoguro, “Computational aerodynamics with isogeometric analysis”, Journal of Mechanics, 39 (2023) 24–39, 10.1093/jom/ufad002
@ARTICLE{Bazilevs22a, AUTHOR = {Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar and A.~Korobenko and T.~Kuraishi and Y.~Otoguro}, PAGES = {24--39}, JOURNAL = {Journal of Mechanics}, VOLUME = {39}, TITLE = {Computational Aerodynamics With Isogeometric Analysis}, YEAR = {2023}, DOI = {10.1093/jom/ufad002} }

[273]

T. Terahara, K. Takizawa, R. Avsar, and T.E. Tezduyar, “T-splines computational membrane–cable structural mechanics with continuity and smoothness: II. Spacecraft parachutes”, Computational Mechanics, 71 (2023) 677–686, 10.1007/s00466-022-02265-9
@ARTICLE{Terahara22c, AUTHOR = {T.~Terahara and K.~Takizawa and R.~Avsar and T. E.~Tezduyar}, PAGES = {677--686}, JOURNAL = {Computational Mechanics}, VOLUME = {71}, TITLE = {T-Splines Computational Membrane--Cable Structural Mechanics with Continuity and Smoothness: {II}. {S}pacecraft parachutes}, YEAR = {2023}, DOI = {10.1007/s00466-022-02265-9} } Abstract:
In this second part of a two-part article, we present spacecraft parachute structural mechanics computations with the T-splines computational method introduced in the first part. The method and its implementation, which was also given in the first part, are for computations where structures with different parametric dimensions are connected with continuity and smoothness. The basis functions of the method were derived in the context of connecting structures with 2D and 1D parametric dimensions. In the first part, the 2D structure was referred to as “membrane” and the 1D structure as “cable.” The method and its implementation, however, are certainly applicable also to other 2D–1D cases, and the test computations presented in the first part included shell–cable structures. Similarly, the spacecraft parachute computations presented here are with both the membrane and shell models of the parachute canopy fabric. The computer model used in the computations is for a subscale, wind-tunnel version of the Disk–Gap–Band parachute. The computations demonstrate the effectiveness of the method in 2D–1D structural mechanics computation of spacecraft parachutes.

[272]

T. Terahara, K. Takizawa, and T.E. Tezduyar, “T-splines computational membrane–cable structural mechanics with continuity and smoothness: I. Method and implementation”, Computational Mechanics, 71 (2023) 657–675, 10.1007/s00466-022-02256-w
@ARTICLE{Terahara22b, AUTHOR = {T.~Terahara and K.~Takizawa and T. E.~Tezduyar}, PAGES = {657--675}, JOURNAL = {Computational Mechanics}, VOLUME = {71}, TITLE = {T-Splines Computational Membrane--Cable Structural Mechanics with Continuity and Smoothness: {I}. {M}ethod and Implementation}, YEAR = {2023}, DOI = {10.1007/s00466-022-02256-w} } Abstract:
We present a T-splines computational method and its implementation where structures with different parametric dimensions are connected with continuity and smoothness. We derive the basis functions in the context of connecting structures with 2D and 1D parametric dimensions. Derivation of the basis functions with a desired smoothness involves proper selection of a scale factor for the knot vector of the 1D structure and results in new control-point locations. While the method description focuses on C and C1 continuity, paths to higher-order continuity are marked where needed. In presenting the method and its implementation, we refer to the 2D structure as “membrane” and the 1D structure as “cable.” It goes without saying that the method and its implementation are applicable also to other 2D–1D cases, such as shell–cable and shell–beam structures. We present test computations not only for membrane–cable structures but also for shell–cable structures. The computations demonstrate how the method performs.

[271]

K. Takizawa, Y. Bazilevs, and T.E. Tezduyar, “Isogeometric discretization methods in computational fluid mechanics”, Mathematical Models and Methods in Applied Sciences, 32 (2022) 2359–2370, 10.1142/S0218202522020018
@ARTICLE{Takizawa22c, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar}, PAGES = {2359--2370}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {32}, TITLE = {Isogeometric Discretization Methods in Computational Fluid Mechanics}, YEAR = {2022}, DOI = {10.1142/S0218202522020018}, NUMBER = {12} } Abstract:
In this lead article of the special issue, we provide a brief summary of the research developments in Isogeometric Analysis (IGA) for Computational Fluid Dynamics (CFD). We focus on the use of IGA in combination with stabilized and variational multiscale methods in fluids. We highlight the key developments and present results in IGA-based CFD that makes this technology attractive for the computational analysis of complex, unsteady and, often turbulent, flows encountered in modern science and engineering applications. We cover both incompressible and compressible flows, numerical method development and performance evaluation using benchmark problems, and applications ranging from stratified environmental flows over complex terrains to concrete-blast fluid–structure interaction. A short synopsis of each article in the special issue is also provided to help reader quickly see what is in the special issue.

[270]

Y. Liu, K. Takizawa, T.E. Tezduyar, T. Kuraishi, and Y. Zhang, “Carrier-domain method for high-resolution computation of time-periodic long-wake flows”, Computational Mechanics, 71 (2022) 169–190, 10.1007/s00466-022-02230-6
@ARTICLE{LiuYang22b, AUTHOR = {Y.~Liu and K.~Takizawa and T. E.~Tezduyar and T.~Kuraishi and Y.~Zhang}, PAGES = {169--190}, JOURNAL = {Computational Mechanics}, VOLUME = {71}, TITLE = {Carrier-Domain Method for High-Resolution Computation of Time-Periodic Long-Wake Flows}, YEAR = {2022}, DOI = {10.1007/s00466-022-02230-6} } Abstract:
© 2022, The Author(s).We are introducing the Carrier-Domain Method (CDM) for high-resolution computation of time-periodic long-wake flows, with cost-effectives that makes the computations practical. The CDM is closely related to the Multidomain Method, which was introduced 24 years ago, originally intended also for cost-effective computation of long-wake flows and later extended in scope to cover additional classes of flow problems. In the CDM, the computational domain moves in the free-stream direction, with a velocity that preserves the outflow nature of the downstream computational boundary. As the computational domain is moving, the velocity at the inflow plane is extracted from the velocity computed earlier when the plane’s current position was covered by the moving domain. The inflow data needed at an instant is extracted from one or more instants going back in time as many periods. Computing the long-wake flow with a high-resolution moving mesh that has a reasonable length would certainly be far more cost-effective than computing it with a fixed mesh that covers the entire length of the wake. We are also introducing a CDM version where the computational domain moves in a discrete fashion rather than a continuous fashion. To demonstrate how the CDM works, we compute, with the version where the computational domain moves in a continuous fashion, the 2D flow past a circular cylinder at Reynolds number 100. At this Reynolds number, the flow has an easily discernible vortex shedding frequency and widely published lift and drag coefficients and Strouhal number. The wake flow is computed up to 350 diameters downstream of the cylinder, far enough to see the secondary vortex street. The computations are performed with the Space–Time Variational Multiscale method and isogeometric discretization; the basis functions are quadratic NURBS in space and linear in time. The results show the power of the CDM in high-resolution computation of time-periodic long-wake flows.

[269]

T. Kuraishi, Z. Xu, K. Takizawa, T.E. Tezduyar, and S. Yamasaki, “High-resolution multi-domain space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation”, Computational Mechanics, 70 (2022) 1257–1279, 10.1007/s00466-022-02228-0
@ARTICLE{Kuraishi22c, AUTHOR = {T.~Kuraishi and Z.~Xu and K.~Takizawa and T. E.~Tezduyar and S.~Yamasaki}, PAGES = {1257--1279}, JOURNAL = {Computational Mechanics}, VOLUME = {70}, TITLE = {High-Resolution Multi-Domain Space--Time Isogeometric Analysis of Car and Tire Aerodynamics with Road Contact and Tire Deformation and Rotation}, YEAR = {2022}, DOI = {10.1007/s00466-022-02228-0} } Abstract:
© 2022, The Author(s).We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems.

[268]

T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Boundary layer mesh resolution in flow computation with the Space–Time Variational Multiscale method and isogeometric discretization”, Mathematical Models and Methods in Applied Sciences, 32 (2022) 2401–2443, 10.1142/S0218202522500567
@ARTICLE{Kuraishi22b, AUTHOR = {T.~Kuraishi and K.~Takizawa and T. E.~Tezduyar}, PAGES = {2401--2443}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {32}, TITLE = {Boundary layer mesh resolution in flow computation with the {S}pace--{T}ime {V}ariational {M}ultiscale method and isogeometric discretization}, YEAR = {2022}, DOI = {10.1142/S0218202522500567}, NUMBER = {12} } Abstract:
We present an extensive study on boundary layer mesh resolution in flow computation with the Space-Time Variational Multiscale (ST-VMS) method and isogeometric discretization. The study is in the context of 2D flow past a circular cylinder, at Reynolds number ranging from 102 to 106. It was motivated by the need to have in tire aerodynamics a better understanding of the mesh resolution requirements near the tire surface. The focus in the study is on the normal-direction element length for the first layer of elements near the cylinder, with that length varying by a refinement factor ranging from 2 to 40. The evaluation is based mostly on the velocity profile near the cylinder. As the element length for the first layer is varied, the element lengths for the other layers of the disk-shaped inner mesh are adjusted, with no increase in the number of elements for the refinement factors 2, 3, and 4, and with modest increases only in the radial direction for refinement factors beyond that. The computations are performed with quadratic NURBS basis functions in space and linear basis functions in time. The expressions for the stabilization parameters used in the ST-VMS and for the related local lengths scales are those targeting isogeometric discretization, introduced in recent years. The mesh resolution study is based mostly on the strong enforcement of the Dirichlet boundary conditions on the cylinder, but also includes some computations with the weakly-enforced conditions. We expect that the data generated and observations made will be helpful in setting proper near-surface mesh resolution in VMS-based computations with isogeometric discretization, not only for cylindrical shapes but also for comparable geometries. We furthermore expect that although the data generated and observations made are based on computations with nonmoving meshes, they will also be applicable to computations with moving meshes where the mesh around the solid surface rotates with the surface in the framework of the ST Slip Interface method.

[267]

Y. Liu, K. Takizawa, Y. Otoguro, T. Kuraishi, and T.E. Tezduyar, “Flow computation with the space–time isogeometric analysis and higher-order basis functions in time”, Mathematical Models and Methods in Applied Sciences, 32 (2022) 2445–2475, 10.1142/S0218202522500579
@ARTICLE{LiuYang22a, AUTHOR = {Y.~Liu and K.~Takizawa and Y.~Otoguro and T.~Kuraishi and T. E.~Tezduyar}, PAGES = {2445--2475}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {32}, TITLE = {Flow Computation with the Space--Time Isogeometric Analysis and Higher-Order Basis Functions in Time}, YEAR = {2022}, DOI = {10.1142/S0218202522500579}, NUMBER = {12} } Abstract:
We present method-evaluation incompressible-flow computations with Space-Time Isogeometric Analysis (ST-IGA) and higher-order basis functions in time. The computational-methods platform is made of the ST Variational Multiscale (ST-VMS) method, the ST-IGA with IGA basis functions in space and time, and local length scales and stabilization parameters targeting isogeometric discretization. The computations are for 2D flow past a circular cylinder at Reynolds number 100, which has an easily discernible vortex shedding frequency and widely published lift and drag coefficients and Strouhal number. We compute with quadratic basis functions in space and polynomial orders of 1, 2, 3, and 4 in time, for four different time-step sizes, and with six different sets of expressions for the stabilization parameters. The computations yield a comprehensive set of method-evaluation data that can serve as reference. They also show computational-cost efficiency in using higher-order functions in time.

[266]

Y. Taniguchi, K. Takizawa, Y. Otoguro, and T.E. Tezduyar, “A hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress: I. Out-of-plane deformation”, Computational Mechanics, 70 (2022) 247–280, 10.1007/s00466-022-02166-x
@ARTICLE{Taniguchi22a, AUTHOR = {Y.~Taniguchi and K.~Takizawa and Y.~Otoguro and T. E.~Tezduyar}, PAGES = {247--280}, JOURNAL = {Computational Mechanics}, VOLUME = {70}, TITLE = {A hyperelastic extended {K}irchhoff--{L}ove shell model with out-of-plane normal stress: {I}. {O}ut-of-plane deformation}, YEAR = {2022}, DOI = {10.1007/s00466-022-02166-x} } Abstract:
© 2022, The Author(s).This is the first part of a two-part article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We present the derivation of the new model, with focus on the mechanics of the out-of-plane deformation. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The improvement is beyond what we get from accounting for the out-of-plane deformation mapping. By accounting for the out-of-plane normal stress, the traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the new model is free from the “midsurface” location in terms of specifying the traction. We also present derivations related to the variation of the kinetic energy and the form of specifying the traction and moment acting on the upper and lower surfaces and along the edges. We present test computations for unidirectional plate bending, plate saddle deformation, and pressurized cylindrical and spherical shells. We use the neo-Hookean and Fung’s material models, for the compressible- and incompressible-material cases, and with the out-of-plane normal stress and without, which is the plane-stress case.

[265]

T. Terahara, T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Computational flow analysis with boundary layer and contact representation: II. Heart valve flow with leaflet contact”, Journal of Mechanics, 38 (2022) 185–194, 10.1093/jom/ufac013
@ARTICLE{Terahara22a, AUTHOR = {T.~Terahara and T.~Kuraishi and K.~Takizawa and T. E.~Tezduyar}, PAGES = {185--194}, JOURNAL = {Journal of Mechanics}, VOLUME = {38}, TITLE = {Computational flow analysis with boundary layer and contact representation: {II}. {H}eart valve flow with leaflet contact}, YEAR = {2022}, DOI = {10.1093/jom/ufac013} } Abstract:
© 2022 The Author(s).In this second part of a two-part article, we provide an overview of the heart valve flow analyses conducted with boundary layer and contact representation, made possible with the space-time (ST) computational methods described in the first part. With these ST methods, we are able to represent the boundary layers near moving solid surfaces, including the valve leaflet surfaces, with the accuracy one gets from moving-mesh methods and without the need for leaving a mesh protection gap between the surfaces coming into contact. The challenge of representing the contact between the leaflets without giving up on high-resolution flow representation near the leaflet surfaces has been overcome. The other challenges that have been overcome include the complexities of a near-actual valve geometry, having in the computational model a left ventricle with an anatomically realistic motion and an aorta from CT scans and maintaining the flow stability at the inflow of the ventricle-valve-aorta sequence, where we have a traction boundary condition during part of the cardiac cycle.

[264]

T. Kuraishi, T. Terahara, K. Takizawa, and T.E. Tezduyar, “Computational flow analysis with boundary layer and contact representation: I. Tire aerodynamics with road contact”, Journal of Mechanics, 38 (2022) 77–87, 10.1093/jom/ufac009
@ARTICLE{Kuraishi22a, AUTHOR = {T.~Kuraishi and T.~Terahara and K.~Takizawa and T. E.~Tezduyar}, PAGES = {77--87}, JOURNAL = {Journal of Mechanics}, VOLUME = {38}, TITLE = {Computational flow analysis with boundary layer and contact representation: {I}. {T}ire aerodynamics with road contact}, YEAR = {2022}, DOI = {10.1093/jom/ufac009} } Abstract:
© 2022 The Author(s).In computational flow analysis with moving solid surfaces and contact between the solid surfaces, it is a challenge to represent the boundary layers with an accuracy attributed to moving-mesh methods and to represent the contact without leaving a mesh protection gap. The space-time topology change (ST-TC) method, introduced in 2013, makes moving-mesh computation possible even when we have contact between moving solid surfaces or other kinds of flow-domain TC. The contact is represented without giving up on high-resolution flow representation near the moving surfaces. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting this class of flow analysis in the presence of additional complexities such as geometric complexity, rotation or deformation of the solid surfaces and the multiscale nature of the flow. In this first part of a two-part article, we provide an overview of the methods that made all that possible. We also provide an overview of the computations performed for tire aerodynamics with challenges that include the complexity of a near-actual tire geometry with grooves, road contact, tire deformation and rotation, road roughness and fluid films.

[263]

T. Kuraishi, S. Yamasaki, K. Takizawa, T.E. Tezduyar, Z. Xu, and R. Kaneko, “Space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation”, Computational Mechanics, 70 (2022) 49–72, 10.1007/s00466-022-02155-0
@ARTICLE{Kuraishi21c, AUTHOR = {T.~Kuraishi and S.~Yamasaki and K.~Takizawa and T. E.~Tezduyar and Z.~Xu and R.~Kaneko}, PAGES = {49--72}, JOURNAL = {Computational Mechanics}, VOLUME = {70}, TITLE = {Space--time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation}, YEAR = {2022}, DOI = {10.1007/s00466-022-02155-0} } Abstract:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.We present a space–time (ST) isogeometric analysis framework for car and tire aerodynamics with road contact and tire deformation and rotation. The geometries of the computational models for the car body and tires are close to the actual geometries. The computational challenges include i) the complexities of these geometries, ii) the tire rotation, iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, iv) the turbulent nature of the flow, v) the aerodynamic interaction between the car body and the tires, and vi) NURBS mesh generation for the complex geometries. The computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) method, and the element-based mesh relaxation (EBMR). The ST context provides higher-order accuracy in general, the VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, and the moving-mesh feature of the ST context enables high-resolution flow computation near the moving fluid–solid interfaces. The ST-SI enables moving-mesh computation with the tire rotating. The mesh covering the tire rotates with it, and the SI between the rotating mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-TC enables moving-mesh computation even with the TC created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the tire and road surfaces. It also enables dealing with the tire–road contact location change and contact sliding. By integrating the ST-IGA with the ST-SI and ST-TC, in addition to having a more accurate representation of the tire geometry and increased accuracy in the flow solution, the element density in the tire grooves and in the narrow spaces near the contact areas is kept at a reasonable level. The NSVGMG enables NURBS mesh generation for the complex car and tire geometries, and the EBMR improves the quality of the meshes. The car and tire aerodynamics computation we present shows the effectiveness of the analysis framework we have built.

[262]

F. Zhang, T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Wind turbine wake computation with the ST-VMS method and isogeometric discretization: Directional preference in spatial refinement”, Computational Mechanics, 69 (2022) 1031–1040, 10.1007/s00466-021-02129-8
@ARTICLE{ZhangFulin21a, AUTHOR = {F.~Zhang and T.~Kuraishi and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1031--1040}, JOURNAL = {Computational Mechanics}, VOLUME = {69}, TITLE = {Wind turbine wake computation with the {ST-VMS} method and isogeometric discretization: {D}irectional preference in spatial refinement}, YEAR = {2022}, DOI = {10.1007/s00466-021-02129-8} } Abstract:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.In this sequel to a two-part article on wind turbine wake computation with the Space–Time Variational Multiscale (ST-VMS) method and ST isogeometric discretization, we study directional preference in spatial refinement. We evaluate the wake computation accuracy of different combinations of mesh resolutions in the free-stream and cross-flow directions. We also evaluate the accuracy of different combinations of B-spline polynomial orders in those directions. The computational framework is the same as in the two-part article. It is made of, in addition to the ST-VMS and ST isogeometric discretization, the Multidomain Method (MDM). It enables accurate representation of the turbine long-wake vortex patterns in a computationally efficient way. Because of the ST context, the computational framework has higher-order accuracy to begin with; because of the VMS feature, it addresses the computational challenges associated with the multiscale nature of the flow; with the isogeometric discretization, it provides increased accuracy in the flow solution; and with the MDM, a long wake can be computed over a sequence of subdomains, instead of a single, long domain, thus reducing the computational cost. Also with the MDM, the computation over a downstream subdomain can start several turbine rotations after the computation over the upstream subdomain starts, thus reducing the computational cost even more. In the computations presented here, as in the two-part article, the velocity data on the inflow plane comes from a previous wind turbine computation, extracted by projection from a plane located 10 m downstream of the turbine, which has a diameter of 126 m. The directional-refinement studies involve four different spatial resolutions, two different B-spline polynomial orders, and two different temporal resolutions. The studies show that there is some preference for refinement in the cross-flow directions.

[261]

T. Kuraishi, F. Zhang, K. Takizawa, and T.E. Tezduyar, “Wind turbine wake computation with the ST-VMS method, isogeometric discretization and multidomain method: II. Spatial and temporal resolution”, Computational Mechanics, 68 (2021) 175–184, 10.1007/s00466-021-02025-1
@ARTICLE{Kuraishi21b, AUTHOR = {T.~Kuraishi and F.~Zhang and K.~Takizawa and T. E.~Tezduyar}, PAGES = {175--184}, JOURNAL = {Computational Mechanics}, VOLUME = {68}, TITLE = {Wind turbine wake computation with the {ST-VMS} method, isogeometric discretization and multidomain method: {II}. {S}patial and temporal resolution}, YEAR = {2021}, DOI = {10.1007/s00466-021-02025-1} } Abstract:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.In this second part of a two-part article, we present extensive studies on spatial and temporal resolution in wind turbine wake computation with the computational framework presented in the first part. The framework, which is made of the Space–Time Variational Multiscale (ST-VMS) method, ST isogeometric discretization, and the Multidomain Method (MDM), enables accurate representation of the turbine long-wake vortex patterns in a computationally efficient way. Because of the ST context, the framework has higher-order accuracy to begin with; because of the VMS feature of the ST-VMS, it addresses the computational challenges associated with the multiscale nature of the flow; with the isogeometric discretization, it provides increased accuracy in the flow solution; and with the MDM, a long wake can be computed over a sequence of subdomains, instead of a single, long domain, thus reducing the computational cost. Also with the MDM, the computation over a downstream subdomain can start several turbine rotations after the computation over the upstream subdomain starts, thus reducing the computational cost even more. In the computations presented here, the velocity data on the inflow plane comes from a previous wind turbine computation, extracted by projection from a plane located 10 m downstream of the turbine, which has a diameter of 126 m. The resolution studies involve three different spatial resolutions and two different temporal resolutions. The studies show that the computational framework provides, with a practical level of efficiency, high-fidelity solutions in wind turbine long-wake computations.

[260]

T. Kuraishi, F. Zhang, K. Takizawa, and T.E. Tezduyar, “Wind turbine wake computation with the ST-VMS method, isogeometric discretization and multidomain method: I. Computational framework”, Computational Mechanics, 68 (2021) 113–130, 10.1007/s00466-021-02022-4
@ARTICLE{Kuraishi21a, AUTHOR = {T.~Kuraishi and F.~Zhang and K.~Takizawa and T. E.~Tezduyar}, PAGES = {113--130}, JOURNAL = {Computational Mechanics}, VOLUME = {68}, TITLE = {Wind turbine wake computation with the {ST-VMS} method, isogeometric discretization and multidomain method: {I}. {C}omputational framework}, YEAR = {2021}, DOI = {10.1007/s00466-021-02022-4} } Abstract:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.In this first part of a two-part article, we present a framework for wind turbine wake computation. The framework is made of the Space–Time Variational Multiscale (ST-VMS) method, ST isogeometric discretization, and the Multidomain Method (MDM). The ST context provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables increased accuracy in the flow solution. With the MDM, a long wake can be computed over a sequence of subdomains, instead of a single, long domain, thus somewhat reducing the computational cost. Furthermore, with the MDM, the computation over a downstream subdomain can start several turbine rotations after the computation over the upstream subdomain starts, thus reducing the computational cost even more. All these good features of the framework, in combination, enable accurate representation of the turbine long-wake vortex patterns in a computationally efficient way. In the computations we present, the velocity data on the inflow plane comes from a previous wind turbine computation, extracted by projection from a plane located 10 m downstream of the turbine, which has a diameter of 126 m. The results show the effectiveness of the framework in wind turbine long-wake computation.

[259]

L. Aydinbakar, K. Takizawa, T.E. Tezduyar, and T. Kuraishi, “Space–time VMS isogeometric analysis of the Taylor–Couette flow”, Computational Mechanics, 67 (2021) 1515–1541, 10.1007/s00466-021-02004-6
@ARTICLE{Aydinbakar21a, AUTHOR = {L.~Aydinbakar and K.~Takizawa and T. E.~Tezduyar and T.~Kuraishi}, PAGES = {1515--1541}, JOURNAL = {Computational Mechanics}, VOLUME = {67}, TITLE = {Space--Time {VMS} Isogeometric Analysis of the {T}aylor--{C}ouette Flow}, YEAR = {2021}, DOI = {10.1007/s00466-021-02004-6} } Abstract:
© 2021, The Author(s).The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

[258]

L. Aydinbakar, K. Takizawa, T.E. Tezduyar, and D. Matsuda, “U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization”, Computational Mechanics, 67 (2021) 823–843, 10.1007/s00466-020-01965-4
@ARTICLE{Aydinbakar20a, AUTHOR = {L.~Aydinbakar and K.~Takizawa and T. E.~Tezduyar and D.~Matsuda}, PAGES = {823--843}, JOURNAL = {Computational Mechanics}, VOLUME = {67}, TITLE = {U-duct turbulent-flow computation with the {ST-VMS} method and isogeometric discretization}, YEAR = {2021}, DOI = {10.1007/s00466-020-01965-4} } Abstract:
© 2021, The Author(s).The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used as the inflow profile. The ST-VMS serves as the core method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The ST isogeometric discretization enables more accurate representation of the duct geometry and increased accuracy in the flow solution. In the straight-duct computations to obtain the inflow velocity, the periodicity condition is enforced with the ST Slip Interface method. All computations are carried out with quadratic NURBS meshes, which represent the circular arc of the duct exactly in the U-duct computations. We investigate how the results vary with the time-averaging range used in reporting the results, mesh refinement, and the Courant number. The results are compared to experimental data, showing that the ST-VMS with ST isogeometric discretization provides good accuracy in this class of flow problems.

[257]

P. Tonon, R.A.K. Sanches, K. Takizawa, and T.E. Tezduyar, “A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion”, Computational Mechanics, 67 (2021) 413–434, 10.1007/s00466-020-01941-y
@ARTICLE{Tonon20a, AUTHOR = {P.~Tonon and R. A. K.~Sanches and K.~Takizawa and T. E.~Tezduyar}, PAGES = {413--434}, JOURNAL = {Computational Mechanics}, VOLUME = {67}, TITLE = {A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion}, YEAR = {2021}, DOI = {10.1007/s00466-020-01941-y} } Abstract:
© 2021, The Author(s).Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels tn and tn+1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at tn. While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

[256]

Y. Bazilevs, K. Takizawa, M.C.H. Wu, T. Kuraishi, R. Avsar, Z. Xu, and T.E. Tezduyar, “Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method”, Computational Mechanics, 67 (2021) 57–84, 10.1007/s00466-020-01919-w
@ARTICLE{Bazilevs20b, AUTHOR = {Y.~Bazilevs and K.~Takizawa and M. C. H.~Wu and T.~Kuraishi and R.~Avsar and Z.~Xu and T. E.~Tezduyar}, PAGES = {57--84}, JOURNAL = {Computational Mechanics}, VOLUME = {67}, TITLE = {Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method}, YEAR = {2021}, DOI = {10.1007/s00466-020-01919-w} } Abstract:
© 2020, The Author(s).A recently introduced NURBS mesh generation method for complex-geometry Isogeometric Analysis (IGA) is applied to building a high-quality mesh for a gas turbine. The compressible flow in the turbine is computed using the IGA and a stabilized method with improved discontinuity-capturing, weakly-enforced no-slip boundary-condition, and sliding-interface operators. The IGA results are compared with the results from the stabilized finite element simulation to reveal superior performance of the NURBS-based approach. Free-vibration analysis of the turbine rotor using the structural mechanics NURBS mesh is also carried out and shows that the NURBS mesh generation method can be used also in structural mechanics analysis. With the flow field from the NURBS-based turbine flow simulation, the Courant number is computed based on the NURBS mesh local length scale in the flow direction to show some of the other positive features of the mesh generation framework. The work presented further advances the IGA as a fully-integrated and robust design-to-analysis framework, and the IGA-based complex-geometry flow computation with moving boundaries and interfaces represents the first of its kind for compressible flows.

[255]

Y. Otoguro, H. Mochizuki, K. Takizawa, and T.E. Tezduyar, “Space–time variational multiscale isogeometric analysis of a tsunami-shelter vertical-axis wind turbine”, Computational Mechanics, 66 (2020) 1443–1460, 10.1007/s00466-020-01910-5
@ARTICLE{Otoguro19b, AUTHOR = {Y.~Otoguro and H.~Mochizuki and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1443--1460}, JOURNAL = {Computational Mechanics}, VOLUME = {66}, TITLE = {Space--Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine}, YEAR = {2020}, DOI = {10.1007/s00466-020-01910-5} } Abstract:
© 2020, The Author(s).We present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of the turbine geometry, multiscale unsteady flow, and moving-boundary flow associated with the rotor motion. The tsunami-shelter VAWT, because of its rather high geometric complexity, poses the additional challenge of reaching high accuracy in turbine-geometry representation and flow solution when the geometry is so complex. We address the challenges with a space–time (ST) computational method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method, and mesh generation and improvement methods. The three special methods are the ST Slip Interface (ST-SI) method, ST Isogeometric Analysis (ST-IGA), and the ST/NURBS Mesh Update Method (STNMUM). The ST-discretization feature of the integrated method provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the blade and other turbine geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex turbine geometry. The quality of the mesh generated with this method is improved with a mesh relaxation method based on fiber-reinforced hyperelasticity and optimized zero-stress state. We present computations for the 2D and 3D cases. The computations show the effectiveness of our ST and mesh generation and relaxation methods in flow analysis of the tsunami-shelter VAWT.

[254]

Y. Ueda, Y. Otoguro, K. Takizawa, and T.E. Tezduyar, “Element-splitting-invariant local-length-scale calculation in B-spline meshes for complex geometries”, Mathematical Models and Methods in Applied Sciences, 30 (2020) 2139–2174, 10.1142/S0218202520500402
@ARTICLE{Ueda20a, AUTHOR = {Y.~Ueda and Y.~Otoguro and K.~Takizawa and T. E.~Tezduyar}, PAGES = {2139--2174}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {30}, TITLE = {Element-Splitting-Invariant Local-Length-Scale Calculation in {B}-Spline Meshes for Complex Geometries}, YEAR = {2020}, DOI = {10.1142/S0218202520500402} } Abstract:
© 2020 The Author(s).Variational multiscale methods and their precursors, stabilized methods, which are sometimes supplemented with discontinuity-capturing (DC) methods, have been playing their core-method role in flow computations increasingly with isogeometric discretization. The stabilization and DC parameters embedded in most of these methods play a significant role. The parameters almost always involve some local-length-scale expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, local-length-scale expressions originally intended for finite element discretization were being used also for isogeometric discretization. The direction-dependent expressions introduced in [Y. Otoguro, K. Takizawa and T. E. Tezduyar, Element length calculation in B-spline meshes for complex geometries, Comput. Mech. 65 (2020) 1085-1103, https://doi.org/10.1007/s00466-019-01809-w] target B-spline meshes for complex geometries. The key stages of deriving these expressions are mapping the direction vector from the physical element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. The expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. Element splitting may be a part of the computational method in a variety of cases, including computations with T-spline discretization and immersed boundary and extended finite element methods and their isogeometric versions. We do not want the element splitting to influence the actual discretization, which is represented by the control or nodal points. Therefore, the local length scale should be invariant with respect to element splitting. In element definition, invariance of the local length scale is a crucial requirement, because, unlike the element definition choices based on implementation convenience or computational efficiency, it influences the solution. We provide a proof, in the context of B-spline meshes, for the element-splitting invariance of the local-length-scale expressions introduced in the above reference.

[253]

K. Takizawa, T.E. Tezduyar, and R. Avsar, “A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state”, Computational Mechanics, 65 (2020) 1567–1591, 10.1007/s00466-020-01835-z
@ARTICLE{Takizawa20b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and R.~Avsar}, PAGES = {1567--1591}, JOURNAL = {Computational Mechanics}, VOLUME = {65}, TITLE = {A Low-Distortion Mesh Moving Method Based on Fiber-Reinforced Hyperelasticity and Optimized Zero-Stress State}, YEAR = {2020}, DOI = {10.1007/s00466-020-01835-z} } Abstract:
© 2020, The Author(s).In computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction, moving-mesh methods enable mesh-resolution control near the interface and consequently high-resolution representation of the boundary layers. Good moving-mesh methods require good mesh moving methods. We introduce a low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state (ZSS). The method has been developed targeting isogeometric discretization but is also applicable to finite element discretization. With the large-deformation mechanics equations, we can expect to have a unique mesh associated with each step of the boundary or interface motion. With the fibers placed in multiple directions, we stiffen the element in those directions for the purpose of reducing the distortion during the mesh deformation. We optimize the ZSS by seeking orthogonality of the parametric directions, by mesh relaxation, and by making the ZSS time-dependent as needed. We present 2D and 3D test computations with isogeometric discretization. The computations show that the mesh moving method introduced performs well.

[252]

A. Castorrini, P. Venturini, A. Corsini, F. Rispoli, K. Takizawa, and T.E. Tezduyar, “Computational analysis of particle-laden-airflow erosion and experimental verification”, Computational Mechanics, 65 (2020) 1549–1565, 10.1007/s00466-020-01834-0
@ARTICLE{Castorrini20a, AUTHOR = {A.~Castorrini and P.~Venturini and A.~Corsini and F.~Rispoli and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1549--1565}, JOURNAL = {Computational Mechanics}, VOLUME = {65}, TITLE = {Computational Analysis of Particle-Laden-Airflow Erosion and Experimental Verification}, YEAR = {2020}, DOI = {10.1007/s00466-020-01834-0} } Abstract:
© 2020, The Author(s).Computational analysis of particle-laden-airflow erosion can help engineers have a better understanding of the erosion process, maintenance and protection of turbomachinery components. We present an integrated method for this class of computational analysis. The main components of the method are the residual-based Variational Multiscale (VMS) method, a finite element particle-cloud tracking (PCT) method with ellipsoidal clouds, an erosion model based on two time scales, and the Solid-Extension Mesh Moving Technique (SEMMT). The turbulent-flow nature of the analysis is addressed with the VMS, the particle-cloud trajectories are calculated based on the time-averaged computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. Because the target-geometry update due to the erosion has a very long time scale compared to the fluid–particle dynamics, the update takes place in a sequence of “evolution steps” representing the impact of the erosion. A scale-up factor, calculated based on the update threshold criterion, relates the erosions and particle counts in the evolution steps to those in the PCT computation. As the target geometry evolves, the mesh is updated with the SEMMT. We present a computation designed to match the sand-erosion experiment we conducted with an aluminum-alloy target. We show that, despite the problem complexities and model assumptions involved, we have a reasonably good agreement between the computed and experimental data.

[251]

T. Terahara, K. Takizawa, T.E. Tezduyar, A. Tsushima, and K. Shiozaki, “Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change”, Computational Mechanics, 65 (2020) 1343–1363, 10.1007/s00466-020-01822-4
@ARTICLE{Terahara19b, AUTHOR = {T.~Terahara and K.~Takizawa and T. E.~Tezduyar and A.~Tsushima and K.~Shiozaki}, PAGES = {1343--1363}, JOURNAL = {Computational Mechanics}, VOLUME = {65}, TITLE = {Ventricle-valve-aorta flow analysis with the {S}pace--{T}ime {I}sogeometric {D}iscretization and {T}opology {C}hange}, YEAR = {2020}, DOI = {10.1007/s00466-020-01822-4} } Abstract:
© 2020, The Author(s).We address the computational challenges of and presents results from ventricle-valve-aorta flow analysis. Including the left ventricle (LV) in the model makes the flow into the valve, and consequently the flow into the aorta, anatomically more realistic. The challenges include accurate representation of the boundary layers near moving solid surfaces even when the valve leaflets come into contact, computation with high geometric complexity, anatomically realistic representation of the LV motion, and flow stability at the inflow boundary, which has a traction condition. The challenges are mainly addressed with a Space–Time (ST) method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method. The three special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The ST-discretization feature of the integrated method, ST-SI-TC-IGA, provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow in the LV, valve and aorta. The moving-mesh feature of the ST framework enables high-resolution computation near the leaflets. The ST-TC enables moving-mesh computation even with the TC created by the contact between the leaflets, dealing with the contact while maintaining high-resolution representation near the leaflets. The ST-IGA provides smoother representation of the LV, valve and aorta surfaces and increased accuracy in the flow solution. The ST-SI connects the separately generated LV, valve and aorta NURBS meshes, enabling easier mesh generation, connects the mesh zones containing the leaflets, enabling a more effective mesh moving, helps the ST-TC deal with leaflet–leaflet contact location change and contact sliding, and helps the ST-TC and ST-IGA keep the element density in the narrow spaces near the contact areas at a reasonable level. The ST-SI-TC-IGA is supplemented with two other special methods in this article. A structural mechanics computation method generates the LV motion from the CT scans of the LV and anatomically realistic values for the LV volume ratio. The Constrained-Flow-Profile (CFP) Traction provides flow stability at the inflow boundary. Test computation with the CFP Traction shows its effectiveness as an inflow stabilization method, and computation with the LV-valve-aorta model shows the effectiveness of the ST-SI-TC-IGA and the two supplemental methods.

[250]

T. Terahara, K. Takizawa, T.E. Tezduyar, Y. Bazilevs, and M.-C. Hsu, “Heart valve isogeometric sequentially-coupled FSI analysis with the space–time topology change method”, Computational Mechanics, 65 (2020) 1167–1187, 10.1007/s00466-019-01813-0
@ARTICLE{Terahara19a, AUTHOR = {T.~Terahara and K.~Takizawa and T. E.~Tezduyar and Y.~Bazilevs and Ming-Chen Hsu}, PAGES = {1167--1187}, JOURNAL = {Computational Mechanics}, VOLUME = {65}, TITLE = {Heart Valve Isogeometric Sequentially-Coupled {FSI} Analysis with the Space--Time Topology Change Method}, YEAR = {2020}, DOI = {10.1007/s00466-019-01813-0} } Abstract:
© 2020, The Author(s).Heart valve fluid–structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method that can address the challenges with an outcome of high-fidelity flow solutions. The SCFSI analysis enables dealing with the fluid and structure parts individually at different steps of the solutions sequence, and also enables using different methods or different mesh resolution levels at different steps. In the isogeometric SCFSI analysis here, the first step is a previously computed (fully) coupled Immersogeometric Analysis FSI of the heart valve with a reasonable flow solution. With the valve leaflet and arterial surface motion coming from that, we perform a new, higher-fidelity fluid mechanics computation with the space–time topology change method and isogeometric discretization. Both the immersogeometric and space–time methods are variational multiscale methods. The computation presented for a bioprosthetic heart valve demonstrates the power of the method introduced.

[249]

Y. Otoguro, K. Takizawa, and T.E. Tezduyar, “Element length calculation in B-spline meshes for complex geometries”, Computational Mechanics, 65 (2020) 1085–1103, 10.1007/s00466-019-01809-w
@ARTICLE{Otoguro19c, AUTHOR = {Y.~Otoguro and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1085--1103}, JOURNAL = {Computational Mechanics}, VOLUME = {65}, TITLE = {Element Length Calculation in {B}-Spline meshes for Complex Geometries}, YEAR = {2020}, DOI = {10.1007/s00466-019-01809-w} } Abstract:
© 2020, The Author(s).Variational multiscale methods, and their precursors, stabilized methods, have been playing a core-method role in semi-discrete and space–time (ST) flow computations for decades. These methods are sometimes supplemented with discontinuity-capturing (DC) methods. The stabilization and DC parameters embedded in most of these methods play a significant role. Various well-performing stabilization and DC parameters have been introduced in both the semi-discrete and ST contexts. The parameters almost always involve some element length expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, stabilization and DC parameters originally intended for finite element discretization were being used also for isogeometric discretization. Recently, element lengths and stabilization and DC parameters targeting isogeometric discretization were introduced for ST and semi-discrete computations, and these expressions are also applicable to finite element discretization. The key stages of deriving the direction-dependent element length expression were mapping the direction vector from the physical (ST or space-only) element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. Targeting B-spline meshes for complex geometries, we introduce here new element length expressions, which are outcome of a clear and convincing derivation and more suitable for element-level evaluation. The new expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. The test computations we present for advection-dominated cases, including 2D computations with complex meshes, show that the proposed element length expressions result in good solution profiles.

[248]

K. Takizawa, Y. Ueda, and T.E. Tezduyar, “A node-numbering-invariant directional length scale for simplex elements”, Mathematical Models and Methods in Applied Sciences, 29 (2019) 2719–2753, 10.1142/S0218202519500581
@ARTICLE{Takizawa19b, AUTHOR = {K.~Takizawa and Y.~Ueda and T. E.~Tezduyar}, PAGES = {2719--2753}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {29}, TITLE = {A Node-Numbering-Invariant Directional Length Scale for Simplex Elements}, YEAR = {2019}, DOI = {10.1142/S0218202519500581} } Abstract:
© 2019 The Author(s).Variational multiscale methods, and their precursors, stabilized methods, have been very popular in flow computations in the past several decades. Stabilization parameters embedded in most of these methods play a significant role. The parameters almost always involve element length scales, most of the time in specific directions, such as the direction of the flow or solution gradient. We require the length scales, including the directional length scales, to have node-numbering invariance for all element types, including simplex elements. We propose a length scale expression meeting that requirement. We analytically evaluate the expression in the context of simplex elements and compared to one of the most widely used length scale expressions and show the levels of noninvariance avoided.

[247]

Y. Yu, Y.J. Zhang, K. Takizawa, T.E. Tezduyar, and T. Sasaki, “Anatomically realistic lumen motion representation in patient-specific space–time isogeometric flow analysis of coronary arteries with time-dependent medical-image data”, Computational Mechanics, 65 (2020) 395–404, 10.1007/s00466-019-01774-4
@ARTICLE{YuYuxuan19a, AUTHOR = {Y.~Yu and Y. J.~Zhang and K.~Takizawa and T. E.~Tezduyar and T.~Sasaki}, PAGES = {395--404}, JOURNAL = {Computational Mechanics}, VOLUME = {65}, TITLE = {Anatomically Realistic Lumen Motion Representation in Patient-Specific Space--Time Isogeometric Flow Analysis of Coronary Arteries with Time-Dependent Medical-Image Data}, YEAR = {2020}, DOI = {10.1007/s00466-019-01774-4} } Abstract:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.Patient-specific computational flow analysis of coronary arteries with time-dependent medical-image data can provide valuable information to doctors making treatment decisions. Reliable computational analysis requires a good core method, high-fidelity space and time discretizations, and an anatomically realistic representation of the lumen motion. The space–time variational multiscale (ST-VMS) method has a good track record as a core method. The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the artery. The moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces. The ST isogeometric analysis is a superior discretization method. With IGA basis functions in space, it enables more accurate representation of the lumen geometry and increased accuracy in the flow solution. With IGA basis functions in time, it enables a smoother representation of the lumen motion and a mesh motion consistent with that. With cubic NURBS in time, we obtain a continuous acceleration from the lumen-motion representation. Here we focus on making the lumen-motion representation anatomically realistic. We present a method to obtain from medical-image data in discrete form an anatomically realistic NURBS representation of the lumen motion, without sudden, unrealistic changes introduced by the higher-order representation. In the discrete projection from the medical-image data to the NURBS representation, we supplement the least-squares terms with two penalty terms, corresponding to the first and second time derivatives of the control-point trajectories. The penalty terms help us avoid the sudden unrealistic changes. The computation we present demonstrates the effectiveness of the method.

[246]

T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Space–time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film”, Computational Mechanics, 64 (2019) 1699–1718, 10.1007/s00466-019-01746-8
@ARTICLE{Kuraishi19b, AUTHOR = {T.~Kuraishi and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1699--1718}, JOURNAL = {Computational Mechanics}, VOLUME = {64}, TITLE = {Space--Time Computational Analysis of Tire Aerodynamics with Actual Geometry, Road Contact, Tire Deformation, Road Roughness and Fluid Film}, YEAR = {2019}, DOI = {10.1007/s00466-019-01746-8} } Abstract:
© 2019, The Author(s).The space–time (ST) computational method “ST-SI-TC-IGA” has recently enabled computational analysis of tire aerodynamics with actual tire geometry, road contact and tire deformation. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). These ST methods played their parts in overcoming the computational challenges, including (i) the complexity of an actual tire geometry with longitudinal and transverse grooves, (ii) the spin of the tire, (iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, and (iv) the turbulent nature of the flow. The combination of the ST-VMS, ST-SI and the ST-IGA has also recently enabled solution of fluid film problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality. This was accomplished with the computational flexibility to go beyond the limitations of the Reynolds-equation model. Here we include and address the computational challenges associated with the road roughness and the fluid film between the tire and the road. The new methods we add to accomplish that include a remedy for the trapped fluid, a method for reducing the number of control points as a space occupied by the fluid shrinks down to a narrow gap, and a method for representing the road roughness. We present computations for a 2D test problem with a straight channel, a simple 2D model of the tire, and a 3D model with actual tire geometry and road roughness. The computations show the effectiveness of our integrated set of ST methods targeting tire aerodynamics.

[245]

Y. Otoguro, K. Takizawa, T.E. Tezduyar, K. Nagaoka, R. Avsar, and Y. Zhang, “Space–time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle”, Computational Mechanics, 64 (2019) 1403–1419, 10.1007/s00466-019-01722-2
@ARTICLE{Otoguro19a, AUTHOR = {Y.~Otoguro and K.~Takizawa and T. E.~Tezduyar and K.~Nagaoka and R.~Avsar and Y.~Zhang}, PAGES = {1403--1419}, JOURNAL = {Computational Mechanics}, VOLUME = {64}, TITLE = {Space--Time {VMS} Flow Analysis of a Turbocharger Turbine with Isogeometric Discretization: Computations with Time-Dependent and Steady-Inflow Representations of the Intake/Exhaust Cycle}, YEAR = {2019}, DOI = {10.1007/s00466-019-01722-2} } Abstract:
© 2019, The Author(s).Many of the computational challenges encountered in turbocharger-turbine flow analysis have been addressed by an integrated set of space–time (ST) computational methods. The core computational method is the ST variational multiscale (ST-VMS) method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST slip interface (ST-SI) method enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST Isogeometric Analysis enables more accurate representation of the turbine geometry and increased accuracy in the flow solution. The ST/NURBS Mesh Update Method enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex geometries involved. An SI also provides mesh generation flexibility in a general context by accurately connecting the two sides of the solution computed over nonmatching meshes, and that is enabling the use of nonmatching NURBS meshes in the computations. The computational analysis needs to cover a full intake/exhaust cycle, which is much longer than the turbine rotation cycle because of high rotation speeds, and the long duration required is an additional computational challenge. As one way of addressing that challenge, we propose here to calculate the turbine efficiency for the intake/exhaust cycle by interpolation from the efficiencies associated with a set of steady-inflow computations at different flow rates. The efficiencies obtained from the computations with time-dependent and steady-inflow representations of the intake/exhaust cycle compare well. This demonstrates that predicting the turbine performance from a set of steady-inflow computations is a good way of addressing the challenge associated with the multiple time scales.

[244]

A. Castorrini, A. Corsini, F. Rispoli, P. Venturini, K. Takizawa, and T.E. Tezduyar, “Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion”, Computational Mechanics, 64 (2019) 1133–1153, 10.1007/s00466-019-01697-0
@ARTICLE{Castorrini19b, AUTHOR = {A.~Castorrini and A.~Corsini and F.~Rispoli and P.~Venturini and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1133--1153}, JOURNAL = {Computational Mechanics}, VOLUME = {64}, TITLE = {Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion}, YEAR = {2019}, DOI = {10.1007/s00466-019-01697-0} } Abstract:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.Wind-turbine blade rain and sand erosion, over long periods of time, can degrade the aerodynamic performance and therefore the power production. Computational analysis of the erosion can help engineers have a better understanding of the maintenance and protection requirements. We present an integrated method for this class of computational analysis. The main components of the method are the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) stabilizations, a finite element particle-cloud tracking method, an erosion model based on two time scales, and the solid-extension mesh moving technique (SEMMT). The turbulent-flow nature of the analysis is handled with a Reynolds-averaged Navier–Stokes model and SUPG/PSPG stabilization, the particle-cloud trajectories are calculated based on the computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. Because the geometry update due to the erosion has a very long time scale compared to the fluid–particle dynamics, the update takes place in a sequence of “evolution steps” representing the impact of the erosion. A scale-up factor, calculated in different ways depending on the update threshold criterion, relates the erosions and particle counts in the evolution steps to those in the fluid–particle simulation. As the blade geometry evolves, the mesh is updated with the SEMMT. We present computational analysis of rain and sand erosion for a wind-turbine blade strip, including a case with actual rainfall data and experimental aerodynamic data for eroded airfoil geometries.

[243]

Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, “Computational analysis methods for complex unsteady flow problems”, Mathematical Models and Methods in Applied Sciences, 29 (2019) 825–838, 10.1142/S0218202519020020
@ARTICLE{Bazilevs19a, AUTHOR = {Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar}, PAGES = {825--838}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {29}, TITLE = {Computational Analysis Methods for Complex Unsteady Flow Problems}, YEAR = {2019}, DOI = {10.1142/S0218202519020020} } Abstract:
© World Scientific Publishing CompanyIn this lead paper of the special issue, we provide a brief summary of the stabilized and multiscale methods in fluid dynamics. We highlight the key features of the stabilized and multiscale scale methods, and variational methods in general, that make these approaches well suited for computational analysis of complex, unsteady flows encountered in modern science and engineering applications. We mainly focus on the recent developments. We discuss application of the variational multiscale (VMS) methods to fluid dynamics problems involving computational challenges associated with high-Reynolds-number flows, wall-bounded turbulent flows, flows on moving domains including subdomains in relative motion, fluid-structure interaction (FSI), and complex-fluid flows with FSI.

[242]

T. Sasaki, K. Takizawa, and T.E. Tezduyar, “Medical-image-based aorta modeling with zero-stress-state estimation”, Computational Mechanics, 64 (2019) 249–271, 10.1007/s00466-019-01669-4
@ARTICLE{Sasaki19a, AUTHOR = {T.~Sasaki and K.~Takizawa and T. E.~Tezduyar}, PAGES = {249--271}, JOURNAL = {Computational Mechanics}, VOLUME = {64}, TITLE = {Medical-Image-Based Aorta Modeling with Zero-Stress-State Estimation}, YEAR = {2019}, DOI = {10.1007/s00466-019-01669-4} } Abstract:
© 2019, The Author(s).Because the medical-image-based geometries used in patient-specific arterial fluid–structure interaction computations do not come from the zero-stress state (ZSS) of the artery, we need to estimate the ZSS required in the computations. The task becomes even more challenging for arteries with complex geometries, such as the aorta. In a method we introduced earlier the estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and fewer elements. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. The method has two main components. 1. An iteration technique, which starts with a calculated ZSS initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the medical-image-based target shape is matched. 2. A design procedure, which is based on the Kirchhoff–Love shell model of the artery, is used for calculating the ZSS initial guess. Here we increase the scope and robustness of the method by introducing a new design procedure for the ZSS initial guess. The new design procedure has two features. (a) An IPB shell-like coordinate system, which increases the scope of the design to general parametrization in the computational space. (b) Analytical solution of the force equilibrium in the normal direction, based on the Kirchhoff–Love shell model, which places proper constraints on the design parameters. This increases the estimation accuracy, which in turn increases the robustness of the iterations and the convergence speed. To show how the new design procedure for the ZSS initial guess performs, we first present 3D test computations with a straight tube and a Y-shaped tube. Then we present a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in the model.

[241]

A. Castorrini, A. Corsini, F. Rispoli, K. Takizawa, and T.E. Tezduyar, “A stabilized ALE method for computational fluid–structure interaction analysis of passive morphing in turbomachinery”, Mathematical Models and Methods in Applied Sciences, 29 (2019) 967–994, 10.1142/S0218202519410057
@ARTICLE{Castorrini19a, AUTHOR = {A.~Castorrini and A.~Corsini and F.~Rispoli and K.~Takizawa and T. E.~Tezduyar}, PAGES = {967--994}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {29}, TITLE = {A stabilized {ALE} method for computational fluid--structure interaction analysis of passive morphing in turbomachinery}, YEAR = {2019}, DOI = {10.1142/S0218202519410057} } Abstract:
© World Scientific Publishing CompanyComputational fluid-structure interaction (FSI) and flow analysis now have a significant role in design and performance evaluation of turbomachinery systems, such as wind turbines, fans, and turbochargers. With increasing scope and fidelity, computational analysis can help improve the design and performance. For example, it can help add a passive morphing attachment (MA) to the blades of an axial fan for the purpose of controlling the blade load and section stall. We present a stabilized Arbitrary Lagrangian-Eulerian (ALE) method for computational FSI analysis of passive morphing in turbomachinery. The main components of the method are the Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) stabilizations in the ALE framework, mesh moving with Jacobian-based stiffening, and block-iterative FSI coupling. The turbulent-flow nature of the analysis is handled with a Reynolds-Averaged Navier-Stokes (RANS) model and SUPG/PSPG stabilization, supplemented with the “DRDJ” stabilization. As the structure moves, the fluid mechanics mesh moves with the Jacobian-based stiffening method, which reduces the deformation of the smaller elements placed near the solid surfaces. The FSI coupling between the blocks of the fully-discretized equation system representing the fluid mechanics, structural mechanics, and mesh moving equations is handled with the block-iterative coupling method. We present two-dimensional (2D) and three-dimensional (3D) computational FSI studies for an MA added to an axial-fan blade. The results from the 2D study are used in determining the spanwise length of the MA in the 3D study.

[240]

T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Space–Time Isogeometric flow analysis with built-in Reynolds-equation limit”, Mathematical Models and Methods in Applied Sciences, 29 (2019) 871–904, 10.1142/S0218202519410021
@ARTICLE{Kuraishi19a, AUTHOR = {T.~Kuraishi and K.~Takizawa and T. E.~Tezduyar}, PAGES = {871--904}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {29}, TITLE = {{S}pace--{T}ime {I}sogeometric Flow Analysis with Built-in {R}eynolds-Equation Limit}, YEAR = {2019}, DOI = {10.1142/S0218202519410021} } Abstract:
© World Scientific Publishing CompanyWe present a space-time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of lubrication fluid dynamics problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality, but with the computational flexibility to go beyond the limitations of the Reynolds-equation model. The key components of the method are the ST Variational Multiscale (ST-VMS) method, ST Isogeometric Analysis (ST-IGA), and the ST Slip Interface (ST-SI) method. The VMS feature of the ST-VMS serves as a numerical stabilization method with a good track record, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid-solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-IGA enables more accurate representation of the solid-surface geometries and increased accuracy in the flow solution in general. With the ST-IGA, even with just one quadratic NURBS element across the gap of the lubrication fluid dynamics problem, we reach a solution quality comparable to that of the Reynolds-equation model. The ST-SI enables moving-mesh computation when the spinning solid surface is noncircular. The mesh covering the solid surface spins with it, retaining the high-resolution representation of the flow near the surface, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. We present detailed 2D test computations to show how the method performs compared to the Reynolds-equation model, compared to finite element discretization, at different circumferential and normal mesh refinement levels, when there is an SI in the mesh, and when the no-slip boundary conditions are weakly-enforced.

[239]

T. Kanai, K. Takizawa, T.E. Tezduyar, K. Komiya, M. Kaneko, K. Hirota, M. Nohmi, T. Tsuneda, M. Kawai, and M. Isono, “Methods for computation of flow-driven string dynamics in a pump and residence time”, Mathematical Models and Methods in Applied Sciences, 29 (2019) 839–870, 10.1142/S021820251941001X
@ARTICLE{Kanai18b, AUTHOR = {T.~Kanai and K.~Takizawa and T. E.~Tezduyar and K.~Komiya and M.~Kaneko and K.~Hirota and M.~Nohmi and T.~Tsuneda and M.~Kawai and M.~Isono}, PAGES = {839--870}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {29}, TITLE = {Methods for Computation of Flow-Driven String Dynamics in a Pump and Residence Time}, YEAR = {2019}, DOI = {10.1142/S021820251941001X} } Abstract:
© World Scientific Publishing CompanyWe present methods for computation of flow-driven string dynamics in a pump and related residence time. The string dynamics computations help us understand how the strings carried by a fluid interact with the pump surfaces, including the blades, and get stuck on or around those surfaces. The residence time computations help us to have a simplified but quick understanding of the string behavior. The core computational method is the Space-Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), a general-purpose NURBS mesh generation method for complex geometries, and a one-way-dependence model for the string dynamics. The ST-IGA with NURBS basis functions in space is used in both fluid mechanics and string structural dynamics. The ST framework provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the turbulent nature of the unsteady flow, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the pump geometry and increased accuracy in the flow solution. The IGA discretization also enables increased accuracy in the structural dynamics solution, as well as smoothness in the string shape and fluid dynamics forces computed on the string. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometry we have here. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small.

[238]

T. Sasaki, K. Takizawa, and T.E. Tezduyar, “Aorta zero-stress state modeling with T-spline discretization”, Computational Mechanics, 63 (2019) 1315–1331, 10.1007/s00466-018-1651-0
@ARTICLE{Sasaki18a, AUTHOR = {T.~Sasaki and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1315--1331}, JOURNAL = {Computational Mechanics}, VOLUME = {63}, TITLE = {Aorta Zero-Stress State Modeling with {T}-Spline Discretization}, YEAR = {2019}, DOI = {10.1007/s00466-018-1651-0} } Abstract:
© 2018, The Author(s).The image-based arterial geometries used in patient-specific arterial fluid–structure interaction (FSI) computations, such as aorta FSI computations, do not come from the zero-stress state (ZSS) of the artery. We propose a method for estimating the ZSS required in the computations. Our estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The method has two main components. (1) An iterative method, which starts with a calculated initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the image-based target shape is matched. (2) A method, which is based on the shell model of the artery, is used for calculating the initial guess. The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. Calculating the initial guess based on the shell model of the artery results in a more realistic initial guess. To show how the new ZSS estimation method performs, we first present 3D test computations with a Y-shaped tube. Then we show a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in our model.

[237]

T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Tire aerodynamics with actual tire geometry, road contact and tire deformation”, Computational Mechanics, 63 (2019) 1165–1185, 10.1007/s00466-018-1642-1
@ARTICLE{Kuraishi18a, AUTHOR = {T.~Kuraishi and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1165--1185}, JOURNAL = {Computational Mechanics}, VOLUME = {63}, TITLE = {Tire Aerodynamics with Actual Tire Geometry, Road Contact and Tire Deformation}, YEAR = {2019}, DOI = {10.1007/s00466-018-1642-1} } Abstract:
© 2018, The Author(s).Tire aerodynamics with actual tire geometry, road contact and tire deformation pose tough computational challenges. The challenges include (1) the complexity of an actual tire geometry with longitudinal and transverse grooves, (2) the spin of the tire, (3) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact and tire deformation, and (4) the turbulent nature of the flow. A new space–time (ST) computational method, “ST-SI-TC-IGA,” is enabling us to address these challenges. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). The VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-SI enables moving-mesh computation with the tire spinning. The mesh covering the tire spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-TC enables moving-mesh computation even with the TC created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the tire and road surfaces. It also enables dealing with the tire–road contact location change and contact sliding. By integrating the ST-IGA with the ST-SI and ST-TC, in addition to having a more accurate representation of the tire geometry and increased accuracy in the flow solution, the element density in the tire grooves and in the narrow spaces near the contact areas is kept at a reasonable level. We present computations with the ST-SI-TC-IGA and two models of flow around a rotating tire with road contact and prescribed deformation. One is a simple 2D model for verification purposes, and one is a 3D model with an actual tire geometry and a deformation pattern provided by the tire company. The computations show the effectiveness of the ST-SI-TC-IGA in tire aerodynamics.

[236]

A. Korobenko, Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, “Computer modeling of wind turbines: 1. ALE-VMS and ST-VMS aerodynamic and FSI analysis”, Archives of Computational Methods in Engineering, 26 (2019) 1059–1099, 10.1007/s11831-018-9292-1
@ARTICLE{Korobenko18b, AUTHOR = {A.~Korobenko and Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1059--1099}, JOURNAL = {Archives of Computational Methods in Engineering}, VOLUME = {26}, TITLE = {Computer modeling of wind turbines: 1. {ALE-VMS} and {ST-VMS} aerodynamic and {FSI} analysis}, YEAR = {2019}, DOI = {10.1007/s11831-018-9292-1} } Abstract:
© 2018, CIMNE, Barcelona, Spain.This is the first part of a two-part article on computer modeling of wind turbines. We describe the recent advances made by our teams in ALE-VMS and ST-VMS computational aerodynamic and fluid–structure interaction (FSI) analysis of wind turbines. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian–Eulerian method. The VMS components are from the residual-based VMS method. The ST-VMS method is the VMS version of the Deforming-Spatial-Domain/Stabilized Space–Time method. The ALE-VMS and ST-VMS serve as the core methods in the computations. They are complemented by special methods that include the ALE-VMS versions for stratified flows, sliding interfaces and weak enforcement of Dirichlet boundary conditions, ST Slip Interface (ST-SI) method, NURBS-based isogeometric analysis, ST/NURBS Mesh Update Method (STNMUM), Kirchhoff–Love shell modeling of wind-turbine structures, and full FSI coupling. The VMS feature of the ALE-VMS and ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow, and the moving-mesh feature of the ALE and ST frameworks enables high-resolution computation near the rotor surface. The ST framework, in a general context, provides higher-order accuracy. The ALE-VMS version for sliding interfaces and the ST-SI enable moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the sliding interface or the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-SI also enables prescribing the fluid velocity at the turbine rotor surface as weakly-enforced Dirichlet boundary condition. The STNMUM enables exact representation of the mesh rotation. The analysis cases reported include both the horizontal-axis and vertical-axis wind turbines, stratified and unstratified flows, standalone wind turbines, wind turbines with tower or support columns, aerodynamic interaction between two wind turbines, and the FSI between the aerodynamics and structural dynamics of wind turbines. Comparisons with experimental data are also included where applicable. The reported cases demonstrate the effectiveness of the ALE-VMS and ST-VMS computational analysis in wind-turbine aerodynamics and FSI.

[235]

T.E. Tezduyar and K. Takizawa, “Space–time computations in practical engineering applications: a summary of the 25-year history”, Computational Mechanics, 63 (2019) 747–753, 10.1007/s00466-018-1620-7
@ARTICLE{Tezduyar18a, AUTHOR = {T. E.~Tezduyar and K.~Takizawa}, PAGES = {747--753}, JOURNAL = {Computational Mechanics}, VOLUME = {63}, TITLE = {Space--time computations in practical engineering applications: A summary of the 25-year history}, YEAR = {2019}, DOI = {10.1007/s00466-018-1620-7} } Abstract:
© 2018, The Author(s).In an article published online in July 2018 it was stated that the algorithm proposed in the article is “enabling practical implementation of the space–time FEM for engineering applications.” In fact, space–time computations in practical engineering applications were already enabled in 1993. We summarize the computations that have taken place since then. These computations started with finite element discretization and are now also with isogeometric discretization. They were all in 3D space and were all carried out on parallel computers. For quarter of a century, these computations brought solution to many classes of complex problems ranging from Orion spacecraft parachutes to wind turbines, from patient-specific cerebral aneurysms to heart valves, from thermo-fluid analysis of ground vehicles and tires to turbocharger turbines and exhaust manifolds.

[234]

K. Takizawa, T.E. Tezduyar, and T. Sasaki, “Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping”, Computational Mechanics, 63 (2019) 681–700, 10.1007/s00466-018-1616-3
@ARTICLE{Takizawa18c, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Sasaki}, PAGES = {681--700}, JOURNAL = {Computational Mechanics}, VOLUME = {63}, TITLE = {Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping}, YEAR = {2019}, DOI = {10.1007/s00466-018-1616-3} } Abstract:
© 2018, The Author(s).We derive a hyperelastic shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid–structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the “midsurface” location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the “midsurface” location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung’s models, for the compressible- and incompressible-material cases, and for two different locations of the “midsurface.” We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.

[233]

T. Kanai, K. Takizawa, T.E. Tezduyar, T. Tanaka, and A. Hartmann, “Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization”, Computational Mechanics, 63 (2019) 301–321, 10.1007/s00466-018-1595-4
@ARTICLE{Kanai18a, AUTHOR = {T.~Kanai and K.~Takizawa and T. E.~Tezduyar and T.~Tanaka and A.~Hartmann}, PAGES = {301--321}, JOURNAL = {Computational Mechanics}, VOLUME = {63}, TITLE = {Compressible-Flow Geometric-Porosity Modeling and Spacecraft Parachute Computation with Isogeometric Discretization}, YEAR = {2019}, DOI = {10.1007/s00466-018-1595-4} } Abstract:
© 2018, The Author(s).One of the challenges in computational fluid–structure interaction (FSI) analysis of spacecraft parachutes is the “geometric porosity,” a design feature created by the hundreds of gaps and slits that the flow goes through. Because FSI analysis with resolved geometric porosity would be exceedingly time-consuming, accurate geometric-porosity modeling becomes essential. The geometric-porosity model introduced earlier in conjunction with the space–time FSI method enabled successful computational analysis and design studies of the Orion spacecraft parachutes in the incompressible-flow regime. Recently, porosity models and ST computational methods were introduced, in the context of finite element discretization, for compressible-flow aerodynamics of parachutes with geometric porosity. The key new component of the ST computational framework was the compressible-flow ST slip interface method, introduced in conjunction with the compressible-flow ST SUPG method. Here, we integrate these porosity models and ST computational methods with isogeometric discretization. We use quadratic NURBS basis functions in the computations reported. This gives us a parachute shape that is smoother than what we get from a typical finite element discretization. In the flow analysis, the combination of the ST framework, NURBS basis functions, and the SUPG stabilization assures superior computational accuracy. The computations we present for a drogue parachute show the effectiveness of the porosity models, ST computational methods, and the integration with isogeometric discretization.

[232]

Y. Otoguro, K. Takizawa, T.E. Tezduyar, K. Nagaoka, and S. Mei, “Turbocharger turbine and exhaust manifold flow computation with the Space–Time Variational Multiscale Method and Isogeometric Analysis”, Computers & Fluids, 179 (2019) 764–776, 10.1016/j.compfluid.2018.05.019
@ARTICLE{Otoguro18a, AUTHOR = {Y.~Otoguro and K.~Takizawa and T. E.~Tezduyar and K.~Nagaoka and S.~Mei}, PAGES = {764--776}, JOURNAL = {Computers \& Fluids}, VOLUME = {179}, TITLE = {Turbocharger turbine and exhaust manifold flow computation with the {S}pace--{T}ime {V}ariational {M}ultiscale {M}ethod and {I}sogeometric {A}nalysis}, YEAR = {2019}, DOI = {10.1016/j.compfluid.2018.05.019} } Abstract:
© 2018 The AuthorsWe address the computational challenges encountered in turbocharger turbine and exhaust manifold flow analysis. The core computational method is the Space–Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), and a general-purpose NURBS mesh generation method for complex geometries. The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the manifold and turbine, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the turbine and manifold geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometries we have here. An SI also provides mesh generation flexibility in a general context by accurately connecting the two sides of the solution computed over nonmatching meshes. That is enabling us to use nonmatching NURBS meshes here. Stabilization parameters and element length definitions play a significant role in the ST-VMS and ST-SI. For the ST-VMS, we use the stabilization parameters introduced recently, and for the ST-SI, the element length definition we are introducing here. The model we actually compute with includes the exhaust gas purifier, which makes the turbine outflow conditions more realistic. We compute the flow for a full intake/exhaust cycle, which is much longer than the turbine rotation cycle because of high rotation speeds, and the long duration required is an additional computational challenge. The computation demonstrates that the methods we use here are very effective in this class of challenging flow analyses.

[231]

K. Takizawa, T.E. Tezduyar, H. Uchikawa, T. Terahara, T. Sasaki, and A. Yoshida, “Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization”, Computers & Fluids, 179 (2019) 790–798, 10.1016/j.compfluid.2018.05.025
@ARTICLE{Takizawa18b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and H.~Uchikawa and T.~Terahara and T.~Sasaki and A.~Yoshida}, PAGES = {790--798}, JOURNAL = {Computers \& Fluids}, VOLUME = {179}, TITLE = {Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization}, YEAR = {2019}, DOI = {10.1016/j.compfluid.2018.05.025} } Abstract:
© 2018 Elsevier LtdWe present detailed studies on mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization. Both factors play a key role in the reliability and practical value of aorta flow analysis. The core computational method is the space–time Variational Multiscale (ST-VMS) method. The other key method is the ST Isogeometric Analysis (ST-IGA). The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the aorta. The ST-IGA provides smoother representation of the aorta and increased accuracy in the flow solution. We conduct the studies for a patient-specific aorta geometry. We determine the level of mesh refinement needed and assess the nature of the flow periodicity reached.

[230]

K. Takizawa, T.E. Tezduyar, and Y. Otoguro, “Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations”, Computational Mechanics, 62 (2018) 1169–1186, 10.1007/s00466-018-1557-x
@ARTICLE{Takizawa17e, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and Y.~Otoguro}, PAGES = {1169--1186}, JOURNAL = {Computational Mechanics}, VOLUME = {62}, TITLE = {Stabilization and discontinuity-capturing parameters for space--time flow computations with finite element and isogeometric discretizations}, YEAR = {2018}, DOI = {10.1007/s00466-018-1557-x} } Abstract:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space–time (ST) computational methods in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

[229]

S. Mittal and T.E. Tezduyar, “Comment on ‘Experimental investigation of Taylor vortex photocatalytic reactor for water purification’”, Chemical Engineering Science, 192 (2018) 1262–1262, 10.1016/j.ces.2017.11.014
@ARTICLE{Mittal17a, AUTHOR = {S.~Mittal and T. E.~Tezduyar}, PAGES = {1262--1262}, JOURNAL = {Chemical Engineering Science}, VOLUME = {192}, TITLE = {Comment on `{E}xperimental investigation of {T}aylor vortex photocatalytic reactor for water purification'}, YEAR = {2018}, DOI = {10.1016/j.ces.2017.11.014} } Abstract:
© 2017 Elsevier LtdComment is provided on Dutta and Ray (2004) to identify the source of the two computational-analysis pictures included in the article.

[228]

Y. Otoguro, K. Takizawa, and T.E. Tezduyar, “Space–time VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method”, Computers & Fluids, 158 (2017) 189–200, 10.1016/j.compfluid.2017.04.017
@ARTICLE{Otoguro16a, AUTHOR = {Y.~Otoguro and K.~Takizawa and T. E.~Tezduyar}, PAGES = {189--200}, JOURNAL = {Computers \& Fluids}, VOLUME = {158}, TITLE = {Space--time {VMS} computational flow analysis with isogeometric discretization and a general-purpose {NURBS} mesh generation method}, YEAR = {2017}, DOI = {10.1016/j.compfluid.2017.04.017} } Abstract:
© 2017 Elsevier LtdThe Space–Time Computational Analysis (STCA) with key components that include the ST Variational Multiscale (ST-VMS) method and ST Isogeometric Analysis (ST-IGA) is being increasingly used in fluid mechanics computations with complex geometries. In such computations, the ST-VMS serves as the core method, complemented by the ST-IGA, and sometimes by additional key components, such as the ST Slip Interface (ST-SI) method. To make the ST-IGA use, and in a wider context the IGA use, even more practical in fluid mechanics computations, NURBS volume mesh generation needs to be easier and as automated as possible. To that end, we present a general-purpose NURBS mesh generation method. The method is based on multi-block structured mesh generation with existing techniques, projection of that mesh to a NURBS mesh made of patches that correspond to the blocks, and recovery of the original model surfaces to the extent they are suitable for accurate and robust fluid mechanics computations. It is expected to retain the refinement distribution and element quality of the multi-block structured mesh that we start with. The flexibility of discretization with the general-purpose mesh generation is supplemented with the ST-SI method, which allows, without loss of accuracy, C−1 continuity between NURBS patches and thus removes the matching requirement between the patches. We present a test computation for a turbocharger turbine and exhaust manifold, which demonstrates that the general-purpose mesh generation method proposed makes the IGA use in fluid mechanics computations even more practical.

[227]

K. Takizawa, T.E. Tezduyar, and T. Kanai, “Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity”, Mathematical Models and Methods in Applied Sciences, 27 (2017) 771–806, 10.1142/S0218202517500166
@ARTICLE{Takizawa17a, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Kanai}, PAGES = {771--806}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {27}, TITLE = {Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity}, YEAR = {2017}, DOI = {10.1142/S0218202517500166} } Abstract:
© 2017 World Scientific Publishing Company.Spacecraft-parachute designs quite often include "geometric porosity" created by the hundreds of gaps and slits that the flow goes through. Computational fluid-structure interaction (FSI) analysis of these parachutes with resolved geometric porosity would be exceedingly challenging, and therefore accurate modeling of the geometric porosity is essential for reliable FSI analysis. The space-time FSI (STFSI) method with the homogenized modeling of geometric porosity has proven to be reliable in computational analysis and design studies of Orion spacecraft parachutes in the incompressible-flow regime. Here we introduce porosity models and ST computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. The main components of the ST computational framework we use are the compressible-flow ST SUPG method, which was introduced earlier, and the compressible-flow ST Slip Interface method, which we introduce here. The computations we present for a drogue parachute show the effectiveness of the porosity models and ST computational methods.

[226]

K. Takizawa, T.E. Tezduyar, T. Terahara, and T. Sasaki, “Heart valve flow computation with the integrated Space–Time VMS, Slip Interface, Topology Change and Isogeometric Discretization methods”, Computers & Fluids, 158 (2017) 176–188, 10.1016/j.compfluid.2016.11.012
@ARTICLE{Takizawa16g2, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Terahara and T.~Sasaki}, PAGES = {176--188}, JOURNAL = {Computers \& Fluids}, VOLUME = {158}, TITLE = {Heart valve flow computation with the integrated {S}pace--{T}ime {VMS}, {S}lip {I}nterface, {T}opology {C}hange and {I}sogeometric {D}iscretization methods}, YEAR = {2017}, DOI = {10.1016/j.compfluid.2016.11.012} } Abstract:
© 2016 Elsevier LtdHeart valve flow computation requires accurate representation of boundary layers near moving solid surfaces, including the valve leaflet surfaces, even when the leaflets come into contact. It also requires dealing with a high level of geometric complexity. We address these computational challenges with a Space–Time (ST) method developed by integrating three special ST methods in the framework of the ST Variational Multiscale (ST-VMS) method. The special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The computations are for a realistic aortic-valve model with prescribed valve leaflet motion and actual contact between the leaflets. The ST-VMS method functions as a moving-mesh method, which maintains high-resolution boundary layer representation near the solid surfaces, including leaflet surfaces. The ST-TC method was introduced for moving-mesh computation of flow problems with TC, such as contact between the leaflets of a heart valve. It deals with the contact while maintaining high-resolution representation near the leaflet surfaces. The ST-SI method was originally introduced to have high-resolution representation of the boundary layers near spinning solid surfaces. The mesh covering a spinning solid surface spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides. In the context of heart valves, the SI connects the sectors of meshes containing the leaflets, enabling a more effective mesh moving. In that context, integration of the ST-SI and ST-TC methods enables high-resolution representation even when the contact is between leaflets that are covered by meshes with SI. It also enables dealing with contact location change or contact and sliding on the SI. By integrating the ST-IGA with the ST-SI and ST-TC methods, in addition to having a more accurate representation of the surfaces and increased accuracy in the flow solution, the element density in the narrow spaces near the contact areas is kept at a reasonable level. Furthermore, because the flow representation in the contact area has a wider support in IGA, the flow computation method becomes more robust. The computations we present for an aortic-valve model with two different modes of prescribed leaflet motion show the effectiveness of the ST-SI-TC-IGA method.

[225]

K. Takizawa, T.E. Tezduyar, and T. Sasaki, “Aorta modeling with the element-based zero-stress state and isogeometric discretization”, Computational Mechanics, 59 (2017) 265–280, 10.1007/s00466-016-1344-5
@ARTICLE{Takizawa16f2, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Sasaki}, PAGES = {265--280}, JOURNAL = {Computational Mechanics}, VOLUME = {59}, TITLE = {Aorta modeling with the element-based zero-stress state and isogeometric discretization}, YEAR = {2017}, DOI = {10.1007/s00466-016-1344-5} } Abstract:
© 2016, Springer-Verlag Berlin Heidelberg.Patient-specific arterial fluid–structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the “opening angle.” 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight-tube configurations. Then we show how the method can be used in a 3D computation where the target geometry is coming from medical image of a human aorta.

[224]

A. Castorrini, A. Corsini, F. Rispoli, P. Venturini, K. Takizawa, and T.E. Tezduyar, “Computational analysis of wind-turbine blade rain erosion”, Computers & Fluids, 141 (2016) 175–183, 10.1016/j.compfluid.2016.08.013
@ARTICLE{Castorrini16b, AUTHOR = {A.~Castorrini and A.~Corsini and F.~Rispoli and P.~Venturini and K.~Takizawa and T. E.~Tezduyar}, PAGES = {175--183}, JOURNAL = {Computers \& Fluids}, VOLUME = {141}, TITLE = {Computational analysis of wind-turbine blade rain erosion}, YEAR = {2016}, DOI = {10.1016/j.compfluid.2016.08.013} } Abstract:
© 2016 Elsevier LtdWind-turbine blade rain erosion damage could be significant if the blades are not protected. This damage would not typically influence the structural integrity of the blades, but it could degrade the aerodynamic performance and therefore the power production. We present computational analysis of rain erosion in wind-turbine blades. The main components of the method used in the analysis are the Streamline-Upwind/Petrov–Galerkin (SUPG) and Pressure-Stabilizing/Petrov–Galerkin (PSPG) stabilizations, a finite element particle-cloud tracking method, and an erosion model. The turbulent-flow nature of the analysis is handled with a RANS model and SUPG/PSPG stabilization, the particle-cloud trajectories are calculated based on the computed flow field and closure models defined for the turbulent dispersion of particles, and one-way dependence is assumed between the flow and particle dynamics. The erosion patterns are then computed based on the particle-cloud data. The patterns are consistent with those observed in the actual wind turbines.

[223]

L. Cardillo, A. Corsini, G. Delibra, F. Rispoli, and T.E. Tezduyar, “Flow analysis of a wave-energy air turbine with the SUPG/PSPG stabilization and Discontinuity-Capturing Directional Dissipation”, Computers & Fluids, 141 (2016) 184–190, 10.1016/j.compfluid.2016.07.011
@ARTICLE{Cardillo16b, AUTHOR = {L.~Cardillo and A.~Corsini and G.~Delibra and F.~Rispoli and T. E.~Tezduyar}, PAGES = {184--190}, JOURNAL = {Computers \& Fluids}, VOLUME = {141}, TITLE = {Flow analysis of a wave-energy air turbine with the {SUPG/PSPG} stabilization and {D}iscontinuity-{C}apturing {D}irectional {D}issipation}, YEAR = {2016}, DOI = {10.1016/j.compfluid.2016.07.011} } Abstract:
© 2016 Elsevier LtdWe present a flow analysis of a wave-energy air turbine, commonly known as Wells turbine. The focus here is on the computational method used in the analysis, based on the Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) stabilizations and the Discontinuity-Capturing Directional Dissipation (DCDD). The SUPG/PSPG stabilization is used rather widely and successfully. The DCDD, first introduced to complement the SUPG/PSPG method in computations of incompressible flows in the presence of sharp solution gradients, was also shown to perform well in standard turbulent-flow test computations when compared to the Smagorinsky Large Eddy Simulation (LES) model. The results obtained in our computational analysis of the Wells turbine here compare favorably to the available experimental data, and this demonstrates that the DCDD method performs well also in turbomachinery flows.

[222]

K. Takizawa, T.E. Tezduyar, and T. Terahara, “Ram-air parachute structural and fluid mechanics computations with the space–time isogeometric analysis (ST-IGA)”, Computers & Fluids, 141 (2016) 191–200, 10.1016/j.compfluid.2016.05.027
@ARTICLE{Takizawa16e, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Terahara}, PAGES = {191--200}, JOURNAL = {Computers \& Fluids}, VOLUME = {141}, TITLE = {Ram-Air Parachute Structural and Fluid Mechanics Computations with the Space--Time Isogeometric Analysis ({ST-IGA})}, YEAR = {2016}, DOI = {10.1016/j.compfluid.2016.05.027} } Abstract:
© 2016 Elsevier LtdWe present a method for structural and fluid mechanics computations of ram-air parachutes. A ram-air parachute is a parafoil inflated by the airflow through the inlets at the leading edge. It has better control and gliding capability than round parachutes. Reliable analysis of ram-air parachutes requires accurate representation of the parafoil geometry, fabric porosity and the complex, multiscale flow behavior involved in this class of problems. The key components of the method are (i) the Space–Time Variational Multiscale (ST-VMS) method, (ii) the version of the ST Slip Interface (ST-SI) method where the SI is between a thin porous structure and the fluid on its two sides, (iii) the ST Isogeometric Analysis (ST-IGA), and (iv) special-purpose NURBS mesh generation techniques for the parachute structure and the flow field inside and outside the parafoil. The ST-VMS method is a stabilized formulation that also serves as a turbulence model and can deal effectively with the complex, multiscale flow behavior. With the ST-SI version for porosity modeling, we deal with the fabric porosity in a fashion consistent with how we deal with the standard SIs and how we enforce the Dirichlet boundary conditions weakly. The ST-IGA, with NURBS basis functions in space, gives us, with relatively few number of unknowns, accurate representation of the parafoil geometry and increased accuracy in the flow solution. The special-purpose mesh generation techniques enable NURBS representation of the structure and fluid domains with significant geometric complexity. The test computations we present are for building a starting parachute shape and a starting flow field associated with that parachute shape, which are the first two key steps in fluid–structure interaction analysis. The computations demonstrate the effectiveness of the method in this class of problems.

[221]

K. Takizawa, T.E. Tezduyar, S. Asada, and T. Kuraishi, “Space–time method for flow computations with slip interfaces and topology changes (ST-SI-TC)”, Computers & Fluids, 141 (2016) 124–134, 10.1016/j.compfluid.2016.05.006
@ARTICLE{Takizawa16d, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and S.~Asada and T.~Kuraishi}, PAGES = {124--134}, JOURNAL = {Computers \& Fluids}, VOLUME = {141}, TITLE = {Space--Time Method for Flow Computations with Slip Interfaces and Topology Changes ({ST-SI-TC})}, YEAR = {2016}, DOI = {10.1016/j.compfluid.2016.05.006} } Abstract:
© 2016 Elsevier LtdThe Space–Time Variational Multiscale (ST-VMS) method was introduced to function as a moving-mesh method. It is the VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It has reasonably good turbulence modeling features and serves as a core computational method. The ST Slip Interface (ST-SI) method was introduced to addresses the challenge involved in high-resolution representation of the boundary layers near spinning solid surfaces. The mesh covering a spinning solid surface spins with it and thus maintains the high-resolution representation near it. The ST-TC method was introduced for moving-mesh computation of flow problems with topology changes, such as contact between solid surfaces. It deals with the TC while maintaining high-resolution boundary layer representation near solid surfaces. The “ST-SI-TC” method we introduce here integrates the ST-SI and ST-TC methods in the ST-VMS framework. It enables accurate flow analysis when we have a spinning solid surface that is in contact with a solid surface. We present two test computations with the ST-SI-TC method, and they are both with models of flow around a rotating tire with road contact and prescribed deformation, one with a 2D model, and one with a 3D model.

[220]

K. Takizawa, T.E. Tezduyar, Y. Otoguro, T. Terahara, T. Kuraishi, and H. Hattori, “Turbocharger flow computations with the Space–Time Isogeometric Analysis (ST-IGA)”, Computers & Fluids, 142 (2017) 15–20, 10.1016/j.compfluid.2016.02.021
@ARTICLE{Takizawa16c, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and Y.~Otoguro and T.~Terahara and T.~Kuraishi and H.~Hattori}, PAGES = {15--20}, JOURNAL = {Computers \& Fluids}, VOLUME = {142}, TITLE = {Turbocharger Flow Computations with the {S}pace--{T}ime {I}sogeometric {A}nalysis ({ST-IGA})}, YEAR = {2017}, DOI = {10.1016/j.compfluid.2016.02.021} } Abstract:
© 2016We focus on turbocharger computational flow analysis with a method that possesses higher accuracy in spatial and temporal representations. In the method we have developed for this purpose, we use a combination of (i) the Space–Time Variational Multiscale (ST-VMS) method, which is a stabilized formulation that also serves as a turbulence model, (ii) the ST Slip Interface (ST-SI) method, which maintains high-resolution representation of the boundary layers near spinning solid surfaces by allowing in a consistent fashion slip at the interface between the mesh covering a spinning surface and the mesh covering the rest of the domain, and (iii) the Isogeometric Analysis (IGA), where we use NURBS basis functions in space and time. The basis functions are spatially higher-order in all representations, and temporally higher-order in representation of the solid-surface and mesh motions. The ST nature of the method gives us higher-order accuracy in the flow solver, and when combined with temporally higher-order basis functions, a more accurate representation of the surface motion, and a mesh motion consistent with that. The spatially higher-order basis functions give us again higher-order accuracy in the flow solver, a more accurate, in some parts exact, representation of the surface geometry, and better representation in evaluating the second-order spatial derivatives. Using NURBS basis functions with a complex geometry is not trivial, however, once we generate the mesh, the computational efficiency is substantially increased. We focus on the turbine part of a turbocharger, but our method can also be applied to the compressor part and thus can be extended to the full turbocharger.

[219]

K. Takizawa, T.E. Tezduyar, and H. Hattori, “Computational analysis of flow-driven string dynamics in turbomachinery”, Computers & Fluids, 142 (2017) 109–117, 10.1016/j.compfluid.2016.02.019
@ARTICLE{Takizawa16b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and H.~Hattori}, PAGES = {109--117}, JOURNAL = {Computers \& Fluids}, VOLUME = {142}, TITLE = {Computational Analysis of Flow-Driven String Dynamics in Turbomachinery}, YEAR = {2017}, DOI = {10.1016/j.compfluid.2016.02.019} } Abstract:
© 2016 Elsevier LtdWe focus on computational analysis of flow-driven string dynamics. The objective is to understand how the strings carried by a fluid interact with the solid surfaces present and get stuck on or around those surfaces. Our target application is turbomachinery, such as understanding how strings get stuck on or around the blades of a fan. The components of the method we developed for this purpose are the Space–Time Variational Multiscale (ST-VMS) and ST Slip Interface (ST-SI) methods for the fluid dynamics, and a one-way-dependence model and the Isogeometric Analysis (IGA) for the string dynamics. The ST-VMS method is the core computational technology and it also has the features of a turbulence model. The ST-SI method allows in a consistent fashion slip at the interface between the mesh covering a spinning solid surface and the mesh covering the rest of the domain, and with this, we maintain high-resolution representation of the boundary layers near spinning solid surfaces such as fan blades. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small. The IGA for the string dynamics gives us not only a higher-order method and smoothness in the structure shape, but also smoothness in the fluid dynamics forces calculated on the string. To demonstrate how the method can be used in computational analysis of flow-driven string dynamics, we present the pilot computations we carried out, for a duct with cylindrical obstacles and for a ventilating fan.

[218]

K. Takizawa, T.E. Tezduyar, T. Kuraishi, S. Tabata, and H. Takagi, “Computational thermo-fluid analysis of a disk brake”, Computational Mechanics, 57 (2016) 965–977, 10.1007/s00466-016-1272-4
@ARTICLE{Takizawa16a, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Kuraishi and S.~Tabata and H.~Takagi}, PAGES = {965--977}, JOURNAL = {Computational Mechanics}, VOLUME = {57}, TITLE = {Computational thermo-fluid analysis of a disk brake}, YEAR = {2016}, DOI = {10.1007/s00466-016-1272-4} } Abstract:
© 2016, Springer-Verlag Berlin Heidelberg.We present computational thermo-fluid analysis of a disk brake, including thermo-fluid analysis of the flow around the brake and heat conduction analysis of the disk. The computational challenges include proper representation of the small-scale thermo-fluid behavior, high-resolution representation of the thermo-fluid boundary layers near the spinning solid surfaces, and bringing the heat transfer coefficient (HTC) calculated in the thermo-fluid analysis of the flow to the heat conduction analysis of the spinning disk. The disk brake model used in the analysis closely represents the actual configuration, and this adds to the computational challenges. The components of the method we have developed for computational analysis of the class of problems with these types of challenges include the Space–Time Variational Multiscale method for coupled incompressible flow and thermal transport, ST Slip Interface method for high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces, and a set of projection methods for different parts of the disk to bring the HTC calculated in the thermo-fluid analysis. With the HTC coming from the thermo-fluid analysis of the flow around the brake, we do the heat conduction analysis of the disk, from the start of the breaking until the disk spinning stops, demonstrating how the method developed works in computational analysis of this complex and challenging problem.

[217]

Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, “New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods”, Mathematical Models and Methods in Applied Sciences, 25 (2015) 2217–2226, 10.1142/S0218202515020029
@ARTICLE{Bazilevs15b, AUTHOR = {Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar}, PAGES = {2217--2226}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {25}, TITLE = {New Directions and Challenging Computations in Fluid Dynamics Modeling with Stabilized and Multiscale Methods}, YEAR = {2015}, DOI = {10.1142/S0218202515020029} } Abstract:
© 2015 World Scientific Publishing Company.In this paper, we provide a brief overview of the development of stabilized and multiscale methods in fluid dynamics. We mainly focus on recent developments and new directions in the variational multiscale (VMS) methods. We also discuss applications of the VMS techniques to fluid dynamics problems involving computational challenges associated with high-Reynolds-number flows, wall-bounded turbulent flows, flows with moving domains including subdomains in relative motion, and free-surface flows.

[216]

K. Takizawa, T.E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan, and K. Montel, “Space–time VMS method for flow computations with slip interfaces (ST-SI)”, Mathematical Models and Methods in Applied Sciences, 25 (2015) 2377–2406, 10.1142/S0218202515400126
@ARTICLE{Takizawa15b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and H.~Mochizuki and H.~Hattori and S.~Mei and L.~Pan and K.~Montel}, PAGES = {2377--2406}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {25}, TITLE = {Space--time {VMS} method for flow computations with slip interfaces ({ST-SI})}, YEAR = {2015}, DOI = {10.1142/S0218202515400126} } Abstract:
© 2015 World Scientific Publishing Company.We present the space-time variational multiscale (ST-VMS) method for flow computations with slip interfaces (ST-SI). The method is intended for fluid-structure interaction (FSI) analysis where one or more of the subdomains contain spinning structures, such as the rotor of a wind turbine, and the subdomains are covered by meshes that do not match at the interface and have slip between them. The mesh covering a subdomain with the spinning structure spins with it, thus maintaining the high-resolution representation of the boundary layers near the structure. The starting point in the development of the method is the version of the arbitrary Lagrangian-Eulerian VMS (ALE-VMS) method designed for computations with "sliding interfaces". Interface terms similar to those in the ALE-VMS version are added to the ST-VMS formulation to account for the compatibility conditions for the velocity and stress. In addition to having a high-resolution representation of the boundary layers, because the ST framework allows NURBS functions in temporal representation of the structure motion, we have exact representation of the circular paths associated with the spinning. The ST-SI method includes versions for cases where the SI is between fluid and solid domains with weakly-imposed Dirichlet conditions for the fluid and for cases where the SI is between a thin porous structure and the fluid on its two sides. Test computations with 2D and 3D models of a vertical-axis wind turbine show the effectiveness of the ST-SI method.

[215]

F. Rispoli, G. Delibra, P. Venturini, A. Corsini, R. Saavedra, and T.E. Tezduyar, “Particle tracking and particle–shock interaction in compressible-flow computations with the V-SGS stabilization and YZβ shock-capturing”, Computational Mechanics, 55 (2015) 1201–1209, 10.1007/s00466-015-1160-3
@ARTICLE{Rispoli15a, AUTHOR = {F.~Rispoli and G.~Delibra and P.~Venturini and A.~Corsini and R.~Saavedra and T. E.~Tezduyar}, PAGES = {1201--1209}, JOURNAL = {Computational Mechanics}, VOLUME = {55}, TITLE = {Particle tracking and particle--shock interaction in compressible-flow computations with the {V-SGS} stabilization and {YZ}$\beta$ shock-capturing}, YEAR = {2015}, DOI = {10.1007/s00466-015-1160-3} } Abstract:
© 2015, Springer-Verlag Berlin Heidelberg.The $$YZ\beta $$YZβ shock-capturing technique, which is residual-based, was introduced in conjunction with the Streamline-Upwind/Petrov–Galerkin (SUPG) formulation of compressible flows in conservation variables. It was later also combined with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables and successfully tested on 2D and 3D computation of inviscid flows with shocks. In this paper we extend that combined method to inviscid flow computations with particle tracking and particle–shock interaction. Particles are tracked individually, assuming one-way dependence between the particle dynamics and the flow. We present two steady-state test computations with particle–shock interaction, one in 2D and one in 3D, and show that the overall method is effective in particle tracking and particle–shock interaction analysis in compressible flows.

[214]

K. Takizawa, T.E. Tezduyar, and T. Kuraishi, “Multiscale ST methods for thermo-fluid analysis of a ground vehicle and its tires”, Mathematical Models and Methods in Applied Sciences, 25 (2015) 2227–2255, 10.1142/S0218202515400072
@ARTICLE{Takizawa15a, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Kuraishi}, PAGES = {2227--2255}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {25}, TITLE = {Multiscale {ST} Methods for Thermo-Fluid Analysis of a Ground Vehicle and its Tires}, YEAR = {2015}, DOI = {10.1142/S0218202515400072} } Abstract:
© 2015 World Scientific Publishing Company.We present the core and special multiscale space-time (ST) methods we developed for thermo-fluid analysis of a ground vehicle and its tires. We also present application of these methods to thermo-fluid analysis of a freight truck and its rear set of tires. The core multiscale ST method is the ST variational multiscale (ST-VMS) formulation of the Navier-Stokes equations of incompressible flows with thermal coupling, which is multiscale in the way the small-scale thermo-fluid behavior is represented in the computations. The special multiscale ST method is spatially multiscale, where the thermo-fluid computation over the global domain with a reasonable mesh refinement is followed by a higher-resolution computation over the local domain containing the rear set of tires, with the boundary and initial conditions coming from the data computed over the global domain. The large amount of time-history data from the global computation is stored using the ST computation technique with continuous representation in time (ST-C), which serves as a data compression technique in this context. In our thermo-fluid analysis, we use a road-surface temperature higher than the free-stream temperature, and a tire-surface temperature that is even higher. We also include in the analysis the heat from the engine and exhaust system, with a reasonably realistic representation of the rate by which that heat transfer takes place as well as the surface geometry of the engine and exhaust system over which the heat transfer occurs. We take into account the heave motion of the truck body. We demonstrate how the spatially multiscale ST method, with higher-refinement mesh in the local domain, substantially increases the accuracy of the computed heat transfer rates from the tires.

[213]

K. Takizawa, T.E. Tezduyar, and R. Kolesar, “FSI modeling of the Orion spacecraft drogue parachutes”, Computational Mechanics, 55 (2015) 1167–1179, 10.1007/s00466-014-1108-z
@ARTICLE{Takizawa14h, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and R.~Kolesar}, PAGES = {1167--1179}, JOURNAL = {Computational Mechanics}, VOLUME = {55}, TITLE = {{FSI} Modeling of the {Orion} Spacecraft Drogue Parachutes}, YEAR = {2015}, DOI = {10.1007/s00466-014-1108-z} } Abstract:
© 2014, Springer-Verlag Berlin Heidelberg.The space–time fluid–structure interaction (STFSI) methods for parachute modeling are now capable of bringing reliable analysis to spacecraft parachutes, which pose formidable computational challenges. A number of special FSI methods targeting spacecraft parachutes complement the STFSI core computational technology in addressing these challenges. Until recently, these challenges were addressed for the Orion spacecraft main parachutes, which are the parachutes used for landing, and in the incompressible-flow regime, which is where the main parachutes operate. At higher altitudes the Orion spacecraft will rely on drogue parachutes. These parachutes have a ribbon construction, and in FSI modeling this creates geometric and flow complexities comparable to those encountered in FSI modeling of the main parachutes, which have a ringsail construction. Like the main parachutes, the drogue parachutes will be used in multiple stages—two reefed stages and a fully-open stage. A reefed stage is where a cable along the parachute skirt constrains the diameter to be less than the diameter in the subsequent stage. After a period of time during the descent at the reefed stage, the cable is cut and the parachute disreefs (i.e. expands) to the next stage. The reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open drogue parachutes. We present the special modeling techniques we devised to address the computational challenges and the results from the computations carried out. The flight envelope of the Orion drogue parachutes includes regions where the Mach number is high enough to require a compressible-flow solver. We present a preliminary fluid mechanics computation for such a case.

[212]

K. Takizawa, T.E. Tezduyar, and A. Buscher, “Space–time computational analysis of MAV flapping-wing aerodynamics with wing clapping”, Computational Mechanics, 55 (2015) 1131–1141, 10.1007/s00466-014-1095-0
@ARTICLE{Takizawa14j, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and A.~Buscher}, PAGES = {1131--1141}, JOURNAL = {Computational Mechanics}, VOLUME = {55}, TITLE = {Space--Time Computational Analysis of {MAV} Flapping-Wing Aerodynamics with Wing Clapping}, YEAR = {2015}, DOI = {10.1007/s00466-014-1095-0} } Abstract:
© 2015, Springer-Verlag Berlin Heidelberg.Computational analysis of flapping-wing aerodynamics with wing clapping was one of the classes of computations targeted in introducing the space–time (ST) interface-tracking method with topology change (ST-TC). The ST-TC method is a new version of the deforming-spatial-domain/stabilized ST (DSD/SST) method, enhanced with a master–slave system that maintains the connectivity of the “parent” fluid mechanics mesh when there is contact between the moving interfaces. With that enhancement and because of its ST nature, the ST-TC method can deal with an actual contact between solid surfaces in flow problems with moving interfaces. It accomplishes that while still possessing the desirable features of interface-tracking (moving-mesh) methods, such as better resolution of the boundary layers. Earlier versions of the DSD/SST method, with effective mesh update, were already able to handle moving-interface problems when the solid surfaces are in near contact or create near TC. Flapping-wing aerodynamics of an actual locust, with the forewings and hindwings crossing each other very close and creating near TC, is an example of successfully computed problems. Flapping-wing aerodynamics of a micro aerial vehicle (MAV) with the wings of an actual locust is another example. Here we show how the ST-TC method enables 3D computational analysis of flapping-wing aerodynamics of an MAV with wing clapping. In the analysis, the wings are brought into an actual contact when they clap. We present results for a model dragonfly MAV.

[211]

K. Takizawa, T.E. Tezduyar, C. Boswell, Y. Tsutsui, and K. Montel, “Special methods for aerodynamic-moment calculations from parachute FSI modeling”, Computational Mechanics, 55 (2015) 1059–1069, 10.1007/s00466-014-1074-5
@ARTICLE{Takizawa14g, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and C.~Boswell and Y.~Tsutsui and K.~Montel}, PAGES = {1059--1069}, JOURNAL = {Computational Mechanics}, VOLUME = {55}, TITLE = {Special Methods for Aerodynamic-Moment Calculations from Parachute {FSI} Modeling}, YEAR = {2015}, DOI = {10.1007/s00466-014-1074-5} } Abstract:
© 2014, Springer-Verlag Berlin Heidelberg.The space–time fluid–structure interaction (STFSI) methods for 3D parachute modeling are now at a level where they can bring reliable, practical analysis to some of the most complex parachute systems, such as spacecraft parachutes. The methods include the Deforming-Spatial-Domain/Stabilized ST method as the core computational technology, and a good number of special FSI methods targeting parachutes. Evaluating the stability characteristics of a parachute based on how the aerodynamic moment varies as a function of the angle of attack is one of the practical analyses that reliable parachute FSI modeling can deliver. We describe the special FSI methods we developed for this specific purpose and present the aerodynamic-moment data obtained from FSI modeling of NASA Orion spacecraft parachutes and Japan Aerospace Exploration Agency (JAXA) subscale parachutes.

[210]

K. Takizawa, T.E. Tezduyar, R. Kolesar, C. Boswell, T. Kanai, and K. Montel, “Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes”, Computational Mechanics, 54 (2014) 1461–1476, 10.1007/s00466-014-1069-2
@ARTICLE{Takizawa14e, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and R.~Kolesar and C.~Boswell and T.~Kanai and K.~Montel}, PAGES = {1461--1476}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {Multiscale Methods for Gore Curvature Calculations from {FSI} Modeling of Spacecraft Parachutes}, YEAR = {2014}, DOI = {10.1007/s00466-014-1069-2} } Abstract:
© 2014, Springer-Verlag Berlin Heidelberg.There are now some sophisticated and powerful methods for computer modeling of parachutes. These methods are capable of addressing some of the most formidable computational challenges encountered in parachute modeling, including fluid–structure interaction (FSI) between the parachute and air flow, design complexities such as those seen in spacecraft parachutes, and operational complexities such as use in clusters and disreefing. One should be able to extract from a reliable full-scale parachute modeling any data or analysis needed. In some cases, however, the parachute engineers may want to perform quickly an extended or repetitive analysis with methods based on simplified models. Some of the data needed by a simplified model can very effectively be extracted from a full-scale computer modeling that serves as a pilot. A good example of such data is the circumferential curvature of a parachute gore, where a gore is the slice of the parachute canopy between two radial reinforcement cables running from the parachute vent to the skirt. We present the multiscale methods we devised for gore curvature calculation from FSI modeling of spacecraft parachutes. The methods include those based on the multiscale sequentially-coupled FSI technique and using NURBS meshes. We show how the methods work for the fully-open and two reefed stages of the Orion spacecraft main and drogue parachutes.

[209]

A. Corsini, F. Rispoli, A.G. Sheard, K. Takizawa, T.E. Tezduyar, and P. Venturini, “A variational multiscale method for particle-cloud tracking in turbomachinery flows”, Computational Mechanics, 54 (2014) 1191–1202, 10.1007/s00466-014-1050-0
@ARTICLE{Corsini14a, AUTHOR = {A.~Corsini and F.~Rispoli and A. G.~Sheard and K.~Takizawa and T. E.~Tezduyar and P.~Venturini}, PAGES = {1191--1202}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {A variational multiscale method for particle-cloud tracking in turbomachinery flows}, YEAR = {2014}, DOI = {10.1007/s00466-014-1050-0} } Abstract:
© 2014, Springer-Verlag Berlin Heidelberg.We present a computational method for simulation of particle-laden flows in turbomachinery. The method is based on a stabilized finite element fluid mechanics formulation and a finite element particle-cloud tracking method. We focus on induced-draft fans used in process industries to extract exhaust gases in the form of a two-phase fluid with a dispersed solid phase. The particle-laden flow causes material wear on the fan blades, degrading their aerodynamic performance, and therefore accurate simulation of the flow would be essential in reliable computational turbomachinery analysis and design. The turbulent-flow nature of the problem is dealt with a Reynolds-Averaged Navier–Stokes model and Streamline-Upwind/Petrov–Galerkin/Pressure-Stabilizing/Petrov–Galerkin stabilization, the particle-cloud trajectories are calculated based on the flow field and closure models for the turbulence–particle interaction, and one-way dependence is assumed between the flow field and particle dynamics. We propose a closure model utilizing the scale separation feature of the variational multiscale method, and compare that to the closure utilizing the eddy viscosity model. We present computations for axial- and centrifugal-fan configurations, and compare the computed data to those obtained from experiments, analytical approaches, and other computational methods.

[208]

K. Takizawa, R. Torii, H. Takagi, T.E. Tezduyar, and X.Y. Xu, “Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates”, Computational Mechanics, 54 (2014) 1047–1053, 10.1007/s00466-014-1049-6
@ARTICLE{Takizawa14m, AUTHOR = {K.~Takizawa and R.~ Torii and H.~ Takagi and T. E.~Tezduyar and X. Y.~Xu}, PAGES = {1047--1053}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates}, YEAR = {2014}, DOI = {10.1007/s00466-014-1049-6} } Abstract:
© 2014, The Author(s).We propose a method for coronary arterial dynamics computation with medical-image-based time-dependent anatomical models. The objective is to improve the computational analysis of coronary arteries for better understanding of the links between the atherosclerosis development and mechanical stimuli such as endothelial wall shear stress and structural stress in the arterial wall. The method has two components. The first one is element-based zero-stress (ZS) state estimation, which is an alternative to prestress calculation. The second one is a “mixed ZS state” approach, where the ZS states for different elements in the structural mechanics mesh are estimated with reference configurations based on medical images coming from different instants within the cardiac cycle. We demonstrate the robustness of the method in a patient-specific coronary arterial dynamics computation where the motion of a thin strip along the arterial surface and two cut surfaces at the arterial ends is specified to match the motion extracted from the medical images.

[207]

K. Takizawa, T.E. Tezduyar, C. Boswell, R. Kolesar, and K. Montel, “FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes”, Computational Mechanics, 54 (2014) 1203–1220, 10.1007/s00466-014-1052-y
@ARTICLE{Takizawa14f, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and C.~Boswell and R.~Kolesar and K.~Montel}, PAGES = {1203--1220}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {{FSI} Modeling of the Reefed Stages and Disreefing of the {Orion} Spacecraft Parachutes}, YEAR = {2014}, DOI = {10.1007/s00466-014-1052-y} } Abstract:
© 2014, Springer-Verlag Berlin Heidelberg.Orion spacecraft main and drogue parachutes are used in multiple stages, starting with a “reefed” stage where a cable along the parachute skirt constrains the diameter to be less than the diameter in the subsequent stage. After a period of time during the descent, the cable is cut and the parachute “disreefs” (i.e. expands) to the next stage. Fluid–structure interaction (FSI) modeling of the reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open spacecraft parachutes. These additional challenges are created by the increased geometric complexities and by the rapid changes in the parachute geometry during disreefing. The computational challenges are further increased because of the added geometric porosity of the latest design of the Orion spacecraft main parachutes. The “windows” created by the removal of panels compound the geometric and flow complexity. That is because the Homogenized Modeling of Geometric Porosity, introduced to deal with the flow through the hundreds of gaps and slits involved in the construction of spacecraft parachutes, cannot accurately model the flow through the windows, which needs to be actually resolved during the FSI computation. In parachute FSI computations, the resolved geometric porosity is significantly more challenging than the modeled geometric porosity, especially in computing the reefed stages and disreefing. Orion spacecraft main and drogue parachutes will both have three stages, with computation of the Stage 1 shape and disreefing from Stage 1 to Stage 2 for the main parachute being the most challenging because of the lowest “reefing ratio” (the ratio of the reefed skirt diameter to the nominal diameter). We present the special modeling techniques and strategies we devised to address the computational challenges encountered in FSI modeling of the reefed stages and disreefing of the main and drogue parachutes. We report, for a single parachute, FSI computation of both reefed stages and both disreefing events for both the main and drogue parachutes. In the case of the main parachute, we also report, for a 2-parachute cluster, FSI computation of the disreefing from Stage 2 to Stage 3. With results from these computations, we demonstrate that we have to a great extent overcome one of the most formidable challenges in FSI modeling of spacecraft parachutes.

[206]

K. Takizawa, T.E. Tezduyar, A. Buscher, and S. Asada, “Space–time fluid mechanics computation of heart valve models”, Computational Mechanics, 54 (2014) 973–986, 10.1007/s00466-014-1046-9
@ARTICLE{Takizawa14i, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and A.~Buscher and S.~Asada}, PAGES = {973--986}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {Space--Time Fluid Mechanics Computation of Heart Valve Models}, YEAR = {2014}, DOI = {10.1007/s00466-014-1046-9} } Abstract:
© 2014, Springer-Verlag Berlin Heidelberg.Fluid mechanics computation of heart valves with an interface-tracking (moving-mesh) method was one of the classes of computations targeted in introducing the space–time (ST) interface tracking method with topology change (ST-TC). The ST-TC method is a new version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It can deal with an actual contact between solid surfaces in flow problems with moving interfaces, while still possessing the desirable features of interface-tracking methods, such as better resolution of the boundary layers. The DSD/SST method with effective mesh update can already handle moving-interface problems when the solid surfaces are in near contact or create near TC, if the “nearness” is sufficiently “near” for the purpose of solving the problem. That, however, is not the case in fluid mechanics of heart valves, as the solid surfaces need to be brought into an actual contact when the flow has to be completely blocked. Here we extend the ST-TC method to 3D fluid mechanics computation of heart valve models. We present computations for two models: an aortic valve with coronary arteries and a mechanical aortic valve. These computations demonstrate that the ST-TC method can bring interface-tracking accuracy to fluid mechanics of heart valves, and can do that with computational practicality.

[205]

Y. Bazilevs, K. Takizawa, T.E. Tezduyar, M.-C. Hsu, N. Kostov, and S. McIntyre, “Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods”, Archives of Computational Methods in Engineering, 21 (2014) 359–398, 10.1007/s11831-014-9119-7
@ARTICLE{Bazilevs14a, AUTHOR = {Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar and Ming-Chen Hsu and N.~Kostov and S.~McIntyre}, PAGES = {359--398}, JOURNAL = {Archives of Computational Methods in Engineering}, VOLUME = {21}, TITLE = {Aerodynamic and {FSI} Analysis of Wind Turbines with the {ALE-VMS} and {ST-VMS} Methods}, YEAR = {2014}, DOI = {10.1007/s11831-014-9119-7} } Abstract:
© 2014, CIMNE, Barcelona, Spain.We provide an overview of the aerodynamic and FSI analysis of wind turbines the first three authors’ teams carried out in recent years with the ALE-VMS and ST-VMS methods. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian–Eulerian (ALE) method. The VMS components are from the residual-based VMS (RBVMS) method. The ST-VMS method is the VMS version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method. The techniques complementing these core methods include weak enforcement of the essential boundary conditions, NURBS-based isogeometric analysis, using NURBS basis functions in temporal representation of the rotor motion, mesh motion and also in remeshing, rotation representation with constant angular velocity, Kirchhoff–Love shell modeling of the rotor-blade structure, and full FSI coupling. The analysis cases include the aerodynamics of standalone wind-turbine rotors, wind-turbine rotor and tower, and the FSI that accounts for the deformation of the rotor blades. The specific wind turbines considered are NREL 5MW, NREL Phase VI and Micon 65/13M, all at full scale, and our analysis for NREL Phase VI and Micon 65/13M includes comparison with the experimental data.

[204]

K. Takizawa, Y. Bazilevs, T.E. Tezduyar, M.-C. Hsu, O. Øiseth, K.M. Mathisen, N. Kostov, and S. McIntyre, “Engineering analysis and design with ALE-VMS and space–time methods”, Archives of Computational Methods in Engineering, 21 (2014) 481–508, 10.1007/s11831-014-9113-0
@ARTICLE{Takizawa14c, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar and Ming-Chen Hsu and O.~{\O}iseth and K. M.~Mathisen and N.~Kostov and S.~McIntyre}, PAGES = {481--508}, JOURNAL = {Archives of Computational Methods in Engineering}, VOLUME = {21}, TITLE = {Engineering Analysis and Design with {ALE-VMS} and Space--Time Methods}, YEAR = {2014}, DOI = {10.1007/s11831-014-9113-0} } Abstract:
© 2014, CIMNE, Barcelona, Spain.Flow problems with moving boundaries and interfaces include fluid–structure interaction (FSI) and a number of other classes of problems, have an important place in engineering analysis and design, and offer some formidable computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian–Eulerian method (ALE-VMS). Since their inception, these two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid–object and fluid–particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid–object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the FSI modeling were increased with the special ALE-VMS and ST FSI techniques targeting each of those classes of problems. This article provides an overview of the core ALE-VMS and ST FSI techniques, their recent versions, and the special ALE-VMS and ST FSI techniques. It also provides examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.

[203]

K. Takizawa, Y. Bazilevs, T.E. Tezduyar, C.C. Long, A.L. Marsden, and K. Schjodt, “ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling”, Mathematical Models and Methods in Applied Sciences, 24 (2014) 2437–2486, 10.1142/S0218202514500250
@ARTICLE{Takizawa14b, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar and C. C.~Long and A. L.~Marsden and K.~Schjodt}, PAGES = {2437--2486}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {24}, TITLE = {{ST} and {ALE-VMS} Methods for Patient-Specific Cardiovascular Fluid Mechanics Modeling}, YEAR = {2014}, DOI = {10.1142/S0218202514500250} } Abstract:
This paper provides a review of the space-time (ST) and Arbitrary Lagrangian-Eulerian (ALE) techniques developed by the first three authors' research teams for patient-specific cardiovascular fluid mechanics modeling, including fluid-structure interaction (FSI). The core methods are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized ST formulation, and the stabilized ST FSI technique. A good number of special techniques targeting cardiovascular fluid mechanics have been developed to be used with the core methods. These include: (i) arterial-surface extraction and boundary condition techniques, (ii) techniques for using variable arterial wall thickness, (iii) methods for calculating an estimated zero-pressure arterial geometry, (iv) techniques for prestressing of the blood vessel wall, (v) mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, (vi) a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, (vii) a scaling technique for specifying a more realistic volumetric flow rate, (viii) techniques for the projection of fluid-structure interface stresses, (ix) a recipe for pre-FSI computations that improve the convergence of the FSI computations, (x) the Sequentially-Coupled Arterial FSI technique and its multiscale versions, (xi) techniques for calculation of the wall shear stress (WSS) and oscillatory shear index (OSI), (xii) methods for stent modeling and mesh generation, (xiii) methods for calculation of the particle residence time, and (xiv) methods for an estimated element-based zero-stress state for the artery. Here we provide an overview of the special techniques for WSS and OSI calculations, stent modeling and mesh generation, and calculation of the residence time with application to pulsatile ventricular assist device (PVAD). We provide references for some of the other special techniques. With results from earlier computations, we show how these core and special techniques work. © 2014 World Scientific Publishing Company.

[202]

K. Takizawa, T.E. Tezduyar, and N. Kostov, “Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV”, Computational Mechanics, 54 (2014) 213–233, 10.1007/s00466-014-0980-x
@ARTICLE{Takizawa14a, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and N.~Kostov}, PAGES = {213--233}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {Sequentially-coupled space--time {FSI} analysis of bio-inspired flapping-wing aerodynamics of an {MAV}}, YEAR = {2014}, DOI = {10.1007/s00466-014-0980-x} } Abstract:
We present a sequentially-coupled space-time (ST) computational fluid-structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/ Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The structural mechanics computations are based on the Kirchhoff-Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust. © 2014 Springer-Verlag Berlin Heidelberg.

[201]

K. Takizawa, T.E. Tezduyar, A. Buscher, and S. Asada, “Space–time interface-tracking with topology change (ST-TC)”, Computational Mechanics, 54 (2014) 955–971, 10.1007/s00466-013-0935-7
@ARTICLE{Takizawa13e, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and A.~Buscher and S.~Asada}, PAGES = {955--971}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {Space--Time Interface-Tracking with Topology Change {(ST-TC)}}, YEAR = {2014}, DOI = {10.1007/s00466-013-0935-7} } Abstract:
© 2013, Springer-Verlag Berlin Heidelberg.To address the computational challenges associated with contact between moving interfaces, such as those in cardiovascular fluid–structure interaction (FSI), parachute FSI, and flapping-wing aerodynamics, we introduce a space–time (ST) interface-tracking method that can deal with topology change (TC). In cardiovascular FSI, our primary target is heart valves. The method is a new version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method, and we call it ST-TC. It includes a master–slave system that maintains the connectivity of the “parent” mesh when there is contact between the moving interfaces. It is an efficient, practical alternative to using unstructured ST meshes, but without giving up on the accurate representation of the interface or consistent representation of the interface motion. We explain the method with conceptual examples and present 2D test computations with models representative of the classes of problems we are targeting.

[200]

K. Takizawa, H. Takagi, T.E. Tezduyar, and R. Torii, “Estimation of element-based zero-stress state for arterial FSI computations”, Computational Mechanics, 54 (2014) 895–910, 10.1007/s00466-013-0919-7
@ARTICLE{Takizawa13d, AUTHOR = {K.~Takizawa and H.~Takagi and T. E.~Tezduyar and R.~Torii}, PAGES = {895--910}, JOURNAL = {Computational Mechanics}, VOLUME = {54}, TITLE = {Estimation of Element-Based Zero-Stress State for Arterial {FSI} Computations}, YEAR = {2014}, DOI = {10.1007/s00466-013-0919-7} } Abstract:
© 2013, Springer-Verlag Berlin Heidelberg.In patient-specific arterial fluid–structure interaction (FSI) computations the image-based arterial geometry comes from a configuration that is not stress-free. We present a method for estimation of element-based zero-stress (ZS) state. The method has three main components. (1) An iterative method, which starts with an initial guess for the ZS state, is used for computing the element-based ZS state such that when a given pressure load is applied, the image-based target shape is matched. (2) A method for straight-tube geometries with single and multiple layers is used for computing the element-based ZS state so that we match the given diameter and longitudinal stretch in the target configuration and the “opening angle.” (3) An element-based mapping between the arterial and straight-tube configurations is used for mapping from the arterial configuration to the straight-tube configuration, and for mapping the estimated ZS state of the straight tube back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. We present a set of test computations to show how the method works.

[199]

K. Takizawa and T.E. Tezduyar, “Space–time computation techniques with continuous representation in time (ST-C)”, Computational Mechanics, 53 (2014) 91–99, 10.1007/s00466-013-0895-y
@ARTICLE{Takizawa13c, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, PAGES = {91--99}, JOURNAL = {Computational Mechanics}, VOLUME = {53}, TITLE = {Space--time computation techniques with continuous representation in time ({ST-C})}, YEAR = {2014}, DOI = {10.1007/s00466-013-0895-y} } Abstract:
We introduce space-time computation techniques with continuous representation in time (ST-C), using temporal NURBS basis functions. This gives us a temporally smooth, NURBS-based solution, which is desirable in some cases, and a more efficient way of dealing with the computed data. We propose two versions of ST-C. In the first version, the smooth solution is extracted by projection from a solution computed with a different temporal representation, typically a discontinuous one. We use a successive projection technique with a small number of temporal NURBS basis functions at each projection, and therefore the extraction can take place as the solution with discontinuous temporal representation is being computed, without storing a large amount of time-history data. This version is not limited to solutions computed with ST techniques. In the second version, the solution with continuous temporal representation is computed directly by using a small number of temporal NURBS basis functions in the variational formulation associated with each time step. © 2013 Springer-Verlag Berlin Heidelberg.

[198]

K. Takizawa, T.E. Tezduyar, J. Boben, N. Kostov, C. Boswell, and A. Buscher, “Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity”, Computational Mechanics, 52 (2013) 1351–1364, 10.1007/s00466-013-0880-5
@ARTICLE{Takizawa13b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and J.~Boben and N.~Kostov and C.~Boswell and A.~Buscher}, PAGES = {1351--1364}, JOURNAL = {Computational Mechanics}, VOLUME = {52}, TITLE = {Fluid--structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity}, YEAR = {2013}, DOI = {10.1007/s00466-013-0880-5} } Abstract:
To increase aerodynamic performance, the geometric porosity of a ringsail spacecraft parachute canopy is sometimes increased, beyond the "rings" and "sails" with hundreds of "ring gaps" and "sail slits." This creates extra computational challenges for fluid-structure interaction (FSI) modeling of clusters of such parachutes, beyond those created by the lightness of the canopy structure, geometric complexities of hundreds of gaps and slits, and the contact between the parachutes of the cluster. In FSI computation of parachutes with such "modified geometric porosity," the flow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the Homogenized Modeling of Geometric Porosity (HMGP), which was introduced to deal with the hundreds of gaps and slits. The flow needs to be actually resolved. All these computational challenges need to be addressed simultaneously in FSI modeling of clusters of spacecraft parachutes with modified geometric porosity. The core numerical technology is the Stabilized Space-Time FSI (SSTFSI) technique, and the contact between the parachutes is handled with the Surface-Edge-Node Contact Tracking (SENCT) technique. In the computations reported here, in addition to the SSTFSI and SENCT techniques and HMGP, we use the special techniques we have developed for removing the numerical spinning component of the parachute motion and for restoring the mesh integrity without a remesh. We present results for 2- and 3-parachute clusters with two different payload models. © 2013 Springer-Verlag Berlin Heidelberg.

[197]

K. Takizawa, T.E. Tezduyar, S. McIntyre, N. Kostov, R. Kolesar, and C. Habluetzel, “Space–time VMS computation of wind-turbine rotor and tower aerodynamics”, Computational Mechanics, 53 (2014) 1–15, 10.1007/s00466-013-0888-x
@ARTICLE{Takizawa13a, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and S.~McIntyre and N.~Kostov and R.~Kolesar and C.~Habluetzel}, PAGES = {1--15}, JOURNAL = {Computational Mechanics}, VOLUME = {53}, TITLE = {Space--time {VMS} computation of wind-turbine rotor and tower aerodynamics}, YEAR = {2014}, DOI = {10.1007/s00466-013-0888-x} } Abstract:
We present the space-time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion. © 2013 Springer-Verlag Berlin Heidelberg.

[196]

M.A. Cruchaga, R.S. Reinoso, M.A. Storti, D.J. Celentano, and T.E. Tezduyar, “Finite element computation and experimental validation of sloshing in rectangular tanks”, Computational Mechanics, 52 (2013) 1301–1312, 10.1007/s00466-013-0877-0
@ARTICLE{Cruchaga13a, AUTHOR = {M. A.~Cruchaga and R. S.~Reinoso and M. A.~Storti and D. J.~Celentano and T. E.~Tezduyar}, PAGES = {1301--1312}, JOURNAL = {Computational Mechanics}, VOLUME = {52}, TITLE = {Finite element computation and experimental validation of sloshing in rectangular tanks}, YEAR = {2013}, DOI = {10.1007/s00466-013-0877-0} } Abstract:
Finite element computation and experimental validation of sloshing in rectangular tanks near the primary and secondary resonance modes are presented. In particular, 2D free-surface evolution is studied. The computational analysis is based on solving the Navier-Stokes equations of incompressible flows with a monolithic solver that includes a stabilized formulation and a Lagrangian tracking technique for updating the free surface. The time-dependent behavior of the numerical and experimental wave heights at different control points are compared, where the experimental data is collected using ultrasonic sensors and a shake table that controls the motion of the rectangular container. © 2013 Springer-Verlag Berlin Heidelberg.

[195]

K. Takizawa and T.E. Tezduyar, “Bringing them down safely”, Mechanical Engineering, 134 (2012) 34–37
@ARTICLE{Takizawa12z, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, PAGES = {34--37}, JOURNAL = {Mechanical Engineering}, VOLUME = {134}, TITLE = {Bringing them down safely}, YEAR = {2012}, NUMBER = {12} }

[194]

K. Takizawa, B. Henicke, A. Puntel, N. Kostov, and T.E. Tezduyar, “Computer modeling techniques for flapping-wing aerodynamics of a locust”, Computers & Fluids, 85 (2013) 125–134, 10.1016/j.compfluid.2012.11.008
@ARTICLE{Takizawa12x, AUTHOR = {K.~Takizawa and B.~Henicke and A.~Puntel and N.~Kostov and T. E.~Tezduyar}, PAGES = {125--134}, JOURNAL = {Computers \& Fluids}, VOLUME = {85}, TITLE = {Computer Modeling Techniques for Flapping-Wing Aerodynamics of a Locust}, YEAR = {2013}, DOI = {10.1016/j.compfluid.2012.11.008} } Abstract:
We present an overview of the special computer modeling techniques we have developed recently for flapping-wing aerodynamics of a locust. The wing motion and deformation data is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The special techniques have been developed around our core computational technique, which is the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The special techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the locust wings. Temporal NURBS basis functions are used also in representation of the motion of the volume meshes computed and in remeshing. In this special-issue paper, we present a condensed version of the material from [1], concentrating on the flapping-motion modeling and computations, and also a temporal-order study from [2]. © 2012 Elsevier Ltd.

[193]

Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, “Challenges and directions in computational fluid–structure interaction”, Mathematical Models and Methods in Applied Sciences, 23 (2013) 215–221, 10.1142/S0218202513400010
@ARTICLE{Bazilevs13b, AUTHOR = {Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar}, PAGES = {215--221}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {23}, TITLE = {Challenges and Directions in Computational Fluid--Structure Interaction}, YEAR = {2013}, DOI = {10.1142/S0218202513400010} } Abstract:
In this lead paper of the special issue, we provide some comments on challenges and directions in computational fluid-structure interaction (FSI). We briefly discuss the significance of computational FSI methods, their components, moving-mesh and nonmoving-mesh methods, mesh moving and remeshing concepts, and FSI coupling techniques. © 2013 World Scientific Publishing Company.

[192]

K. Takizawa, K. Schjodt, A. Puntel, N. Kostov, and T.E. Tezduyar, “Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms”, Computational Mechanics, 51 (2013) 1061–1073, 10.1007/s00466-012-0790-y
@ARTICLE{Takizawa12w, AUTHOR = {K.~Takizawa and K.~Schjodt and A.~Puntel and N.~Kostov and T. E.~Tezduyar}, PAGES = {1061--1073}, JOURNAL = {Computational Mechanics}, VOLUME = {51}, TITLE = {Patient-Specific Computational Analysis of the Influence of a Stent on the Unsteady Flow in Cerebral Aneurysms}, YEAR = {2013}, DOI = {10.1007/s00466-012-0790-y} } Abstract:
We present a patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. The analysis is based on four different arterial models extracted form medical images, and the stent is placed across the neck of the aneurysm to reduce the flow circulation in the aneurysm. The core computational technique used in the analysis is the space-time (ST) version of the variational multiscale (VMS) method and is called "DSD/SST-VMST". The special techniques developed for this class of cardiovascular fluid mechanics computations are used in conjunction with the DSD/SST-VMST technique. The special techniques include NURBS representation of the surface over which the stent model and mesh are built, mesh generation with a reasonable resolution across the width of the stent wire and with refined layers of mesh near the arterial and stent surfaces, modeling the double-stent case, and quantitative assessment of the flow circulation in the aneurysm. We provide a brief overview of the special techniques, compute the unsteady flow patterns in the aneurysm for the four arterial models, and investigate in each case how those patterns are influenced by the presence of single and double stents. © 2012 Springer-Verlag.

[191]

K. Takizawa, D. Montes, S. McIntyre, and T.E. Tezduyar, “Space–time VMS methods for modeling of incompressible flows at high Reynolds numbers”, Mathematical Models and Methods in Applied Sciences, 23 (2013) 223–248, 10.1142/s0218202513400022
@ARTICLE{Takizawa12g, AUTHOR = {K.~Takizawa and D.~Montes and S.~McIntyre and T. E.~Tezduyar}, PAGES = {223--248}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {23}, TITLE = {Space--Time {VMS} Methods for Modeling of Incompressible Flows at High {R}eynolds Numbers}, YEAR = {2013}, DOI = {10.1142/s0218202513400022} } Abstract:
Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation was developed for flow problems with moving interfaces and has been successfully applied to some of the most complex problems in that category. A new version of the DSD/SST method for incompressible flows, which has additional subgrid-scale representation features, is the space-time version of the residual-based variational multiscale (VMS) method. This new version, called DSD/SST-VMST and also Space-Time VMS (ST-VMS), provides a more comprehensive framework for the VMS method. We describe the ST-VMS method, including the embedded stabilization parameters, and assess its performance in computation of flow problems at high Reynolds numbers by comparing the results to experimental data. The computations, which include those with 3D airfoil geometries and spacecraft configurations, signal a promising future for the ST-VMS method. © 2013 World Scientific Publishing Company.

[190]

K. Takizawa, D. Montes, M. Fritze, S. McIntyre, J. Boben, and T.E. Tezduyar, “Methods for FSI modeling of spacecraft parachute dynamics and cover separation”, Mathematical Models and Methods in Applied Sciences, 23 (2013) 307–338, 10.1142/S0218202513400058
@ARTICLE{Takizawa12f, AUTHOR = {K.~Takizawa and D.~Montes and M.~Fritze and S.~McIntyre and J.~Boben and T. E.~Tezduyar}, PAGES = {307--338}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {23}, TITLE = {Methods for {FSI} modeling of spacecraft parachute dynamics and cover separation}, YEAR = {2013}, DOI = {10.1142/S0218202513400058} } Abstract:
Fluid-structure interaction (FSI) modeling of spacecraft parachutes involves a number of computational challenges beyond those encountered in a typical FSI problem. The stabilized space-time FSI (SSTFSI) technique serves as a robust and accurate core FSI method, and a number of special FSI methods address the computational challenges specific to spacecraft parachutes. Some spacecraft FSI problems involve even more specific computational challenges and require additional special methods. An example of that is the impulse ejection and parachute extraction of a protective cover used in a spacecraft. The computational challenges specific to this problem are related to the sudden changes in the parachute loads and sudden separation of the cover with very little initial clearance from the spacecraft. We describe the core and special FSI methods, and present the methods we use in FSI analysis of the parachute dynamics and cover separation, including the temporal NURBS representation in modeling the separation motion. © 2013 World Scientific Publishing Company.

[189]

A. Corsini, F. Rispoli, A.G. Sheard, and T.E. Tezduyar, “Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations”, Computational Mechanics, 50 (2012) 695–705, 10.1007/s00466-012-0789-4
@ARTICLE{Corsini12a, AUTHOR = {A.~Corsini and F.~Rispoli and A. G.~Sheard and T. E.~Tezduyar}, PAGES = {695--705}, JOURNAL = {Computational Mechanics}, VOLUME = {50}, TITLE = {Computational Analysis of Noise Reduction Devices in Axial Fans with Stabilized Finite Element Formulations}, YEAR = {2012}, DOI = {10.1007/s00466-012-0789-4} } Abstract:
The paper illustrates how a computational fluid mechanic technique, based on stabilized finite element formulations, can be used in analysis of noise reduction devices in axial fans. Among the noise control alternatives, the study focuses on the use of end-plates fitted at the blade tips to control the leakage flow and the related aeroacoustic sources. The end-plate shape is configured to govern the momentum transfer to the swirling flow at the blade tip. This flow control mechanism has been found to have a positive link to the fan aeroacoustics. The complex physics of the swirling flow at the tip, developing under the influence of the end-plate, is governed by the rolling up of the jet-like leakage flow. The RANS modelling used in the computations is based on the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov- Galerkin methods, supplemented with the DRDJ stabilization. Judicious determination of the stabilization parameters involved is also a part of our computational technique and is described for each component of the stabilized formulation. We describe the flow physics underlying the design of the noise control device and illustrate the aerodynamic performance. Then we investigate the numerical performance of the formulation by analysing the inner workings of the stabilization operators and of their interaction with the turbulence model. © 2012 Springer-Verlag.

[188]

K. Takizawa, M. Fritze, D. Montes, T. Spielman, and T.E. Tezduyar, “Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity”, Computational Mechanics, 50 (2012) 835–854, 10.1007/s00466-012-0761-3
@ARTICLE{Takizawa12e, AUTHOR = {K.~Takizawa and M.~Fritze and D.~Montes and T.~Spielman and T. E.~Tezduyar}, PAGES = {835--854}, JOURNAL = {Computational Mechanics}, VOLUME = {50}, TITLE = {Fluid--structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity}, YEAR = {2012}, DOI = {10.1007/s00466-012-0761-3} } Abstract:
Fluid-structure interaction (FSI) modeling of parachutes poses a number of computational challenges. These include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of ringsail parachutes the geometric porosity created by the construction of the canopy from "rings" and "sails" with hundreds of "ring gaps" and "sail slits," in the case of parachute clusters the contact between the parachutes, and "disreefing" from one stage to another when the parachute is used in multiple stages. The Team for Advanced Flow Simulation and Modeling (Ta*AFSM) has been successfully addressing these computational challenges with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the Ta*AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the Ta*AFSM, which are applicable to cases with nonmatching fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light. The special technique used in dealing with the geometric complexities of the rings and sails is the homogenized modeling of geometric porosity (HMGP), which was developed and improved in recent years by the Ta*AFSM. The surface-edge-node contact tracking (SENCT) technique was introduced by the Ta*AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the Ta*AFSM. As an additional computational challenge, the parachute canopy might, by design, have some of its panels and sails removed. In FSI computation of parachutes with such "modified geometric porosity," the flow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the HMGP and needs to be actually resolved during the FSI computation. In this paper we focus on parachute disreefing, including the disreefing of parachute clusters, and parachutes with modified geometric porosity, including the reefed stages of such parachutes. We describe the additional special techniques we have developed to address the challenges involved and report FSI computations for parachutes and parachute clusters with disreefing and modified geometric porosity. © 2012 Springer-Verlag.

[187]

K. Takizawa, K. Schjodt, A. Puntel, N. Kostov, and T.E. Tezduyar, “Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent”, Computational Mechanics, 50 (2012) 675–686, 10.1007/s00466-012-0760-4
@ARTICLE{Takizawa12d, AUTHOR = {K.~Takizawa and K.~Schjodt and A.~Puntel and N.~Kostov and T. E.~Tezduyar}, PAGES = {675--686}, JOURNAL = {Computational Mechanics}, VOLUME = {50}, TITLE = {Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent}, YEAR = {2012}, DOI = {10.1007/s00466-012-0760-4} } Abstract:
We present the special arterial fluid mechanics techniques we have developed for patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. These techniques are used in conjunction with the core computational technique, which is the space-time version of the variational multiscale (VMS) method and is called "DST/SST-VMST." The special techniques include using NURBS for the spatial representation of the surface over which the stent mesh is built, mesh generation techniques for both the finite- and zero-thickness representations of the stent, techniques for generating refined layers of mesh near the arterial and stent surfaces, and models for representing double stent. We compute the unsteady flow patterns in the aneurysm and investigate how those patterns are influenced by the presence of single and double stents. We also compare the flow patterns obtained with the finite- and zero-thickness representations of the stent. © 2012 Springer-Verlag.

[186]

K. Takizawa, N. Kostov, A. Puntel, B. Henicke, and T.E. Tezduyar, “Space–time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle”, Computational Mechanics, 50 (2012) 761–778, 10.1007/s00466-012-0758-y
@ARTICLE{Takizawa12c, AUTHOR = {K.~Takizawa and N.~Kostov and A.~Puntel and B.~Henicke and T. E.~Tezduyar}, PAGES = {761--778}, JOURNAL = {Computational Mechanics}, VOLUME = {50}, TITLE = {Space--time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle}, YEAR = {2012}, DOI = {10.1007/s00466-012-0758-y} } Abstract:
We present a detailed computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle (MAV). The computational techniques used include the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, which serves as the core computational technique. The DSD/SST formulation is a moving-mesh technique, and in the computations reported here we use the space-time version of the residual-based variational multiscale (VMS) method, which is called "DSD/ SST-VMST." The motion and deformation of the wings are based on data extracted from the high-speed, multi-camera video recordings of a locust in a wind tunnel. A set of special space-time techniques are also used in the computations in conjunction with the DSD/SST method. The special techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the wings and for the mesh moving and remeshing. The computational analysis starts with the computation of the base case, and includes computations with increased temporal and spatial resolutions compared to the base case. In increasing the temporal resolution, we separately test increasing the temporal order, the number of temporal subdivisions, and the frequency of remeshing. In terms of the spatial resolution, we separately test increasing the wing-mesh refinement in the normal and tangential directions and changing the way node connectivities are handled at the wingtips. The computational analysis also includes using different combinations of wing configurations for the MAV and investigating the beneficial and disruptive interactions between the wings and the role of wing camber and twist. © 2012 Springer-Verlag.

[185]

K. Takizawa, B. Henicke, A. Puntel, N. Kostov, and T.E. Tezduyar, “Space–time techniques for computational aerodynamics modeling of flapping wings of an actual locust”, Computational Mechanics, 50 (2012) 743–760, 10.1007/s00466-012-0759-x
@ARTICLE{Takizawa12b, AUTHOR = {K.~Takizawa and B.~Henicke and A.~Puntel and N.~Kostov and T. E.~Tezduyar}, PAGES = {743--760}, JOURNAL = {Computational Mechanics}, VOLUME = {50}, TITLE = {Space--Time Techniques for Computational Aerodynamics Modeling of Flapping Wings of an Actual Locust}, YEAR = {2012}, DOI = {10.1007/s00466-012-0759-x} } Abstract:
We present the special space-time computational techniques we have introduced recently for computational aerodynamics modeling of flapping wings of an actual locust. These techniques have been designed to be used with the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, which is the core computational technique. The DSD/SST formulation was developed for flow problems with moving interfaces and was elevated to newer versions over the years, including the space-time version of the residual-based variational multiscale (VMS) method, which is called "DSD/SST-VMST" and used in the computations reported here. The special space-time techniques are based on using, in the space-time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the locust wings. The motion and deformation data is extracted from the high-speed, multi-camera video recordings of a locust in a wind tunnel. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. These ingredients provide an accurate and efficient way of dealing with the wind tunnel data and the mesh. The computations demonstrate the effectiveness of the core and special space-time techniques in modeling the aerodynamics of flapping wings, with the wing motion and deformation coming from an actual locust. © 2012 Springer-Verlag.

[184]

P.A. Kler, L.D. Dalcin, R.R. Paz, and T.E. Tezduyar, “SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems”, Computational Mechanics, 51 (2013) 171–185, 10.1007/s00466-012-0712-z
@ARTICLE{Kler12a, AUTHOR = {P. A.~Kler and L. D.~Dalcin and R. R.~Paz and T. E.~Tezduyar}, PAGES = {171--185}, JOURNAL = {Computational Mechanics}, VOLUME = {51}, TITLE = {{SUPG} and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems}, YEAR = {2013}, DOI = {10.1007/s00466-012-0712-z} } Abstract:
Electrophoresis is the motion of charged particles relative to the surrounding liquid under the influence of an external electric field. This electrochemical transport process is used in many scientific and technological areas to separate chemical species. Modeling and simulation of electrophoretic transport enables a better understanding of the physicochemical processes developed during the electrophoretic separations and the optimization of various parameters of the electrophoresis devices and their performance. Electrophoretic transport is a multiphysics and multiscale problem. Mass transport, fluid mechanics, electric problems, and their interactions have to be solved in domains with length scales ranging from nanometers to centimeters. We use a finite element method for the computations. Without proper numerical stabilization, computation of coupled fluid mechanics, electrophoretic transport, and electric problems would suffer from spurious oscillations that are related to the high values of the local Péclet and Reynolds numbers and the nonzero divergence of the migration field. To overcome these computational challenges, we propose a stabilized finite element method based on the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation and discontinuity-capturing techniques. To demonstrate the effectiveness of the stabilized formulation, we present test computations with 1D, 2D, and 3D electrophoretic transport problems of technological interest. © 2012 Springer-Verlag.

[183]

Y. Bazilevs, M.-C. Hsu, K. Takizawa, and T.E. Tezduyar, “ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid–structure interaction”, Mathematical Models and Methods in Applied Sciences, 22 (2012) 1230002, 10.1142/S0218202512300025
@ARTICLE{Bazilevs12a, AUTHOR = {Y.~Bazilevs and Ming-Chen Hsu and K.~Takizawa and T. E.~Tezduyar}, PAGES = {1230002}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {22}, TITLE = {{ALE-VMS} and {ST-VMS} Methods for Computer Modeling of Wind-Turbine Rotor Aerodynamics and Fluid--Structure Interaction}, YEAR = {2012}, DOI = {10.1142/S0218202512300025}, NUMBER = {supp02} } Abstract:
We provide an overview of the Arbitrary LagrangianEulerian Variational Multiscale (ALE-VMS) and SpaceTime Variational Multiscale (ST-VMS) methods we have developed for computer modeling of wind-turbine rotor aerodynamics and fluidstructure interaction (FSI). The related techniques described include weak enforcement of the essential boundary conditions, KirchhoffLove shell modeling of the rotor-blade structure, NURBS-based isogeometric analysis, and full FSI coupling. We present results from application of these methods to computer modeling of NREL 5MW and NREL Phase VI wind-turbine rotors at full scale, including comparison with experimental data. © 2012 World Scientific Publishing Company.

[182]

K. Takizawa and T.E. Tezduyar, “Space–time fluid–structure interaction methods”, Mathematical Models and Methods in Applied Sciences, 22 (2012) 1230001, 10.1142/S0218202512300013
@ARTICLE{Takizawa12a, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, PAGES = {1230001}, JOURNAL = {Mathematical Models and Methods in Applied Sciences}, VOLUME = {22}, TITLE = {Space--Time Fluid--Structure Interaction Methods}, YEAR = {2012}, DOI = {10.1142/S0218202512300013}, NUMBER = {supp02} } Abstract:
Since its introduction in 1991 for computation of flow problems with moving boundaries and interfaces, the Deforming-Spatial-Domain/Stabilized SpaceTime (DSD/SST) formulation has been applied to a diverse set of challenging problems. The classes of problems computed include free-surface and two-fluid flows, fluidobject, fluidparticle and fluidstructure interaction (FSI), and flows with mechanical components in fast, linear or rotational relative motion. The DSD/SST formulation, as a core technology, is being used for some of the most challenging FSI problems, including parachute modeling and arterial FSI. Versions of the DSD/SST formulation introduced in recent years serve as lower-cost alternatives. More recent variational multiscale (VMS) version, which is called DSD/SST-VMST (and also ST-VMS), has brought better computational accuracy and serves as a reliable turbulence model. Special spacetime FSI techniques introduced for specific classes of problems, such as parachute modeling and arterial FSI, have increased the scope and accuracy of the FSI modeling in those classes of computations. This paper provides an overview of the core spacetime FSI technique, its recent versions, and the special spacetime FSI techniques. The paper includes test computations with the DSD/SST-VMST technique. © 2012 World Scientific Publishing Company.

[181]

K. Takizawa, Y. Bazilevs, and T.E. Tezduyar, “Space–time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling”, Archives of Computational Methods in Engineering, 19 (2012) 171–225, 10.1007/s11831-012-9071-3
@ARTICLE{Takizawa11n, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar}, PAGES = {171--225}, JOURNAL = {Archives of Computational Methods in Engineering}, VOLUME = {19}, TITLE = {Space--Time and {ALE-VMS} Techniques for Patient-Specific Cardiovascular Fluid--Structure Interaction Modeling}, YEAR = {2012}, DOI = {10.1007/s11831-012-9071-3} } Abstract:
This is an extensive overview of the core and special space-time and Arbitrary Lagrangian-Eulerian (ALE) techniques developed by the authors' research teams for patient-specific cardiovascular fluid-structure interaction (FSI) modeling. The core techniques are the ALE-based variational multiscale (ALE-VMS) method, the Deforming-Spatial-Domain/Stabilized Space-Time formulation, and the stabilized space-time FSI technique. The special techniques include methods for calculating an estimated zero-pressure arterial geometry, prestressing of the blood vessel wall, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI technique and its multiscale versions, techniques for the projection of fluid-structure interface stresses, calculation of the wall shear stress and oscillatory shear index, arterial-surface extraction and boundary condition techniques, and a scaling technique for specifying a more realistic volumetric flow rate. With results from earlier computations, we show how these core and special FSI techniques work in patient-specific cardiovascular simulations. © 2012 CIMNE, Barcelona, Spain.

[180]

K. Takizawa and T.E. Tezduyar, “Computational methods for parachute fluid–structure interactions”, Archives of Computational Methods in Engineering, 19 (2012) 125–169, 10.1007/s11831-012-9070-4
@ARTICLE{Takizawa11m, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, PAGES = {125--169}, JOURNAL = {Archives of Computational Methods in Engineering}, VOLUME = {19}, TITLE = {Computational Methods for Parachute Fluid--Structure Interactions}, YEAR = {2012}, DOI = {10.1007/s11831-012-9070-4} } Abstract:
The computational challenges posed by fluid-structure interaction (FSI) modeling of parachutes include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of "ringsail" parachutes the geometric complexities created by the construction of the canopy from "rings" and "sails" with hundreds of ring "gaps" and sail "slits", and in the case of parachute clusters the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T*AFSM) has successfully addressed these computational challenges with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the T*AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the T*AFSM, which are applicable to cases with incompatible fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light and therefore more sensitive to the variations in the fluid dynamics forces. The special technique used in dealing with the geometric complexities of the rings and sails is the Homogenized Modeling of Geometric Porosity, which was developed and improved in recent years by the T*AFSM. The Surface-Edge-Node Contact Tracking (SENCT) technique was introduced by the T*AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the T*AFSM. We provide an overview of the core and special techniques developed by the T*AFSM, present single-parachute FSI computations carried out for design-parameter studies, and report FSI computation and dynamical analysis of two-parachute clusters. © 2012 CIMNE, Barcelona, Spain.

[179]

A. Corsini, F. Rispoli, and T.E. Tezduyar, “Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique”, Journal of Applied Mechanics, 79 (2012) 010910, 10.1115/1.4005060
@ARTICLE{Corsini11a, AUTHOR = {A.~Corsini and F.~Rispoli and T. E.~Tezduyar}, PAGES = {010910}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {79}, TITLE = {Computer modeling of wave-energy air turbines with the {SUPG/PSPG} formulation and discontinuity-capturing technique}, YEAR = {2012}, DOI = {10.1115/1.4005060} } Abstract:
We present a computational fluid mechanics technique for modeling of wave-energy air turbines, specifically the Wells turbine. In this type of energy conversion, the wave motion is converted to an oscillating airflow in a duct with the turbine. This is a self-rectifying turbine in the sense that it maintains the same direction of rotation as the airflow changes direction. The blades of the turbine are symmetrical, and here we consider straight and swept blades, both with constant chord. The turbulent flow physics involved in the complex, unsteady flow is governed by nonequilibrium behavior, and we use a stabilized formulation to address the related challenges in the context of RANS modeling. The formulation is based on the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin methods, supplemented with the DRDJ stabilization. Judicious determination of the stabilization parameters involved is also a part of our computational technique and is described for each component of the stabilized formulation. We compare the numerical performance of the formulation with and without the DRDJ stabilization and present the computational results obtained for the two blade configurations with realistic airflow data. Copyright © 2012 by ASME.

[178]

S. Takase, K. Kashiyama, S. Tanaka, and T.E. Tezduyar, “Space–time SUPG finite element computation of shallow-water flows with moving shorelines”, Computational Mechanics, 48 (2011) 293–306, 10.1007/s00466-011-0618-1
@ARTICLE{Kashiyama11a, AUTHOR = {S.~Takase and K.~Kashiyama and S.~Tanaka and T. E.~Tezduyar}, PAGES = {293--306}, JOURNAL = {Computational Mechanics}, VOLUME = {48}, TITLE = {Space--Time {SUPG} Finite Element Computation of Shallow-Water Flows with Moving Shorelines}, YEAR = {2011}, DOI = {10.1007/s00466-011-0618-1} } Abstract:
We show that combination of the Deforming-Spatial-Domain/Stabilized Space-Time and the Streamline-Upwind/Petrov-Galerkin formulations can be used quite effectively for computation of shallow-water flows with moving shorelines. The combined formulation is supplemented with a stabilization parameter that was originally introduced for compressible flows, a compressible-flow shock-capturing parameter adapted for shallow-water flows, and remeshing based on using a background mesh. We present a number of test computations and provide comparisons to theoretical results, experimental data and results computed with nonmoving meshes. © 2011 Springer-Verlag.

[177]

M. Manguoglu, K. Takizawa, A.H. Sameh, and T.E. Tezduyar, “A parallel sparse algorithm targeting arterial fluid mechanics computations”, Computational Mechanics, 48 (2011) 377–384, 10.1007/s00466-011-0619-0
@ARTICLE{Manguoglu11a, AUTHOR = {M.~Manguoglu and K.~Takizawa and A. H.~Sameh and T. E.~Tezduyar}, PAGES = {377--384}, JOURNAL = {Computational Mechanics}, VOLUME = {48}, TITLE = {A parallel sparse algorithm targeting arterial fluid mechanics computations}, YEAR = {2011}, DOI = {10.1007/s00466-011-0619-0} } Abstract:
Iterative solution of large sparse nonsymmetric linear equation systems is one of the numerical challenges in arterial fluid-structure interaction computations. This is because the fluid mechanics parts of the fluid + structure block of the equation system that needs to be solved at every nonlinear iteration of each time step corresponds to incompressible flow, the computational domains include slender parts, and accurate wall shear stress calculations require boundary layer mesh refinement near the arterial walls. We propose a hybrid parallel sparse algorithm, domain-decomposing parallel solver (DDPS), to address this challenge. As the test case, we use a fluid mechanics equation system generated by starting with an arterial shape and flow field coming from an FSI computation and performing two time steps of fluid mechanics computation with a prescribed arterial shape change, also coming from the FSI computation. We show how the DDPS algorithm performs in solving the equation system and demonstrate the scalability of the algorithm. © 2011 Springer-Verlag.

[176]

K. Takizawa, B. Henicke, D. Montes, T.E. Tezduyar, M.-C. Hsu, and Y. Bazilevs, “Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics”, Computational Mechanics, 48 (2011) 647–657, 10.1007/s00466-011-0614-5
@ARTICLE{Takizawa11f, AUTHOR = {K.~Takizawa and B.~Henicke and D.~Montes and T. E.~Tezduyar and Ming-Chen Hsu and Y.~Bazilevs}, PAGES = {647--657}, JOURNAL = {Computational Mechanics}, VOLUME = {48}, TITLE = {Numerical-Performance Studies for the Stabilized Space--Time Computation of Wind-Turbine Rotor Aerodynamics}, YEAR = {2011}, DOI = {10.1007/s00466-011-0614-5} } Abstract:
We present our numerical-performance studies for 3D wind-turbine rotor aerodynamics computation with the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. As the test case, we use the NREL 5MW offshore baseline wind-turbine rotor. We compute the problem with both the original version of the DSD/SST formulation and the version with an advanced turbulence model. The DSD/SST formulation with the turbulence model is a recently-introduced space-time version of the residual-based variational multiscale method. We include in our comparison as reference solution the results obtained with the residual-based variational multiscale Arbitrary Lagrangian-Eulerian method using NURBS for spatial discretization. We test different levels of mesh refinement and different definitions for the stabilization parameter embedded in the "least squares on incompressibility constraint" stabilization. We compare the torque values obtained. © 2011 Springer-Verlag.

[175]

K. Takizawa, B. Henicke, A. Puntel, T. Spielman, and T.E. Tezduyar, “Space–time computational techniques for the aerodynamics of flapping wings”, Journal of Applied Mechanics, 79 (2012) 010903, 10.1115/1.4005073
@ARTICLE{Takizawa11e, AUTHOR = {K.~Takizawa and B.~Henicke and A.~Puntel and T.~Spielman and T. E.~Tezduyar}, PAGES = {010903}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {79}, TITLE = {Space--time computational techniques for the aerodynamics of flapping wings}, YEAR = {2012}, DOI = {10.1115/1.4005073} } Abstract:
We present the special space-time computational techniques we have introduced recently for computation of flow problems with moving and deforming solid surfaces. The techniques have been designed in the context of the deforming-spatial-domain/stabilized space-time formulation, which was developed by the Team for Advanced Flow Simulation and Modeling for computation of flow problems with moving boundaries and interfaces. The special space-time techniques are based on using, in the space-time flow computations, non-uniform rational B-splines (NURBS) basis functions for the temporal representation of the motion and deformation of the solid surfaces and also for the motion and deformation of the volume meshes computed. This provides a better temporal representation of the solid surfaces and a more effective way of handling the volume-mesh motion. We apply these techniques to computation of the aerodynamics of flapping wings, specifically locust wings, where the prescribed motion and deformation of the wings are based on digital data extracted from the videos of the locust in a wind tunnel. We report results from the preliminary computations. © 2012 American Society of Mechanical Engineers.

[174]

K. Takizawa, T. Brummer, T.E. Tezduyar, and P.R. Chen, “A comparative study based on patient-specific fluid–structure interaction modeling of cerebral aneurysms”, Journal of Applied Mechanics, 79 (2012) 010908, 10.1115/1.4005071
@ARTICLE{Takizawa11d, AUTHOR = {K.~Takizawa and T.~Brummer and T. E.~Tezduyar and P. R.~Chen}, PAGES = {010908}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {79}, TITLE = {A comparative study based on patient-specific fluid--structure interaction modeling of cerebral aneurysms}, YEAR = {2012}, DOI = {10.1115/1.4005071} } Abstract:
We present an extensive comparative study based on patient-specific fluid-structure interaction (FSI) modeling of cerebral aneurysms. We consider a total of ten cases, at three different locations, half of which ruptured. We use the stabilized space-time FSI technique developed by the Team for Advanced Flow Simulation and Modeling (T AFSM), together with a number of special techniques targeting arterial FSI modeling, which were also developed by the T AFSM. What we look at in our comparisons includes the wall shear stress, oscillatory shear index and the arterial-wall stress and stretch. We also investigate how simpler approaches to computer modeling of cerebral aneurysms perform compared to FSI modeling. © 2012 American Society of Mechanical Engineers.

[173]

K. Takizawa, T. Spielman, C. Moorman, and T.E. Tezduyar, “Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design”, Journal of Applied Mechanics, 79 (2012) 010907, 10.1115/1.4005070
@ARTICLE{Takizawa11c, AUTHOR = {K.~Takizawa and T.~Spielman and C.~ Moorman and T. E.~Tezduyar}, PAGES = {010907}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {79}, TITLE = {Fluid--structure interaction modeling of spacecraft parachutes for simulation-based design}, YEAR = {2012}, DOI = {10.1115/1.4005070} } Abstract:
Even though computer modeling of spacecraft parachutes involves a number of numerical challenges, advanced techniques developed in recent years for fluid-structure interaction (FSI) modeling in general and for parachute FSI modeling specifically have made simulation-based design studies possible. In this paper we focus on such studies for a single main parachute to be used with the Orion spacecraft. Although these large parachutes are typically used in clusters of two or three parachutes, studies for a single parachute can still provide valuable information for performance analysis and design and can be rather extensive. The major challenges in computer modeling of a single spacecraft parachute are the FSI between the air and the parachute canopy and the geometric complexities created by the construction of the parachute from rings and sails with hundreds of gaps and slits. The Team for Advanced Flow Simulation and Modeling has successfully addressed the computational challenges related to the FSI and geometric complexities, and has also been devising special procedures as needed for specific design parameter studies. In this paper we present parametric studies based on the suspension line length, canopy loading, and the length of the overinflation control line. © 2012 American Society of Mechanical Engineers.

[172]

K. Takizawa, T. Spielman, and T.E. Tezduyar, “Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters”, Computational Mechanics, 48 (2011) 345–364, 10.1007/s00466-011-0590-9
@ARTICLE{Takizawa11b, AUTHOR = {K.~Takizawa and T.~Spielman and T. E.~Tezduyar}, PAGES = {345--364}, JOURNAL = {Computational Mechanics}, VOLUME = {48}, TITLE = {Space--time {FSI} modeling and dynamical analysis of spacecraft parachutes and parachute clusters}, YEAR = {2011}, DOI = {10.1007/s00466-011-0590-9} } Abstract:
Computer modeling of spacecraft parachutes, which are quite often used in clusters of two or three large parachutes, involves fluid-structure interaction (FSI) between the parachute canopy and the air, geometric complexities created by the construction of the parachute from "rings" and "sails" with hundreds of gaps and slits, and the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T*AFSM) has successfully addressed the computational challenges related to the FSI and geometric complexities, and recently started addressing the challenges related to the contact between the parachutes of a cluster. The core numerical technology is the stabilized space-time FSI technique developed and improved over the years by the (T*AFSM) . The special technique used in dealing with the geometric complexities is the Homogenized Modeling of Geometric Porosity, which was also developed and improved in recent years by the (T*AFSM) . In this paper we describe the technique developed by the (T*AFSM) for modeling, in the context of an FSI problem, the contact between two structural surfaces. We show how we use this technique in dealing with the contact between parachutes. We present the results obtained with the FSI computation of parachute clusters, the related dynamical analysis, and a special decomposition technique for parachute descent speed to make that analysis more informative. We also present a special technique for extracting from a parachute FSI computation model parameters, such as added mass, that can be used in fast, approximate engineering analysis models for parachute dynamics. © 2011 Springer-Verlag.

[171]

K. Takizawa, B. Henicke, T.E. Tezduyar, M.-C. Hsu, and Y. Bazilevs, “Stabilized space–time computation of wind-turbine rotor aerodynamics”, Computational Mechanics, 48 (2011) 333–344, 10.1007/s00466-011-0589-2
@ARTICLE{Takizawa11a, AUTHOR = {K.~Takizawa and B.~Henicke and T. E.~Tezduyar and Ming-Chen Hsu and Y.~Bazilevs}, PAGES = {333--344}, JOURNAL = {Computational Mechanics}, VOLUME = {48}, TITLE = {Stabilized Space--Time Computation of Wind-Turbine Rotor Aerodynamics}, YEAR = {2011}, DOI = {10.1007/s00466-011-0589-2} } Abstract:
We show how we use the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation for accurate 3D computation of the aerodynamics of a wind-turbine rotor. As the test case, we use the NREL 5MW offshore baseline wind-turbine rotor. This class of computational problems are rather challenging, because they involve large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. We compute the problem with both the original version of the DSD/SST formulation and a recently introduced version with an advanced turbulence model. The DSD/SST formulation with the advanced turbulence model is a space-time version of the residual-based variational multiscale method. We compare our results to those reported recently, which were obtained with the residual-based variational multiscale Arbitrary Lagrangian-Eulerian method using NURBS for spatial discretization and which we take as the reference solution. While the original DSD/SST formulation yields torque values not far from the reference solution, the DSD/SST formulation with the variational multiscale turbulence model yields torque values very close to the reference solution. © 2011 Springer-Verlag.

[170]

K. Takizawa and T.E. Tezduyar, “Multiscale space–time fluid–structure interaction techniques”, Computational Mechanics, 48 (2011) 247–267, 10.1007/s00466-011-0571-z
@ARTICLE{Takizawa10b, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, PAGES = {247--267}, JOURNAL = {Computational Mechanics}, VOLUME = {48}, TITLE = {Multiscale Space--Time Fluid--Structure Interaction Techniques}, YEAR = {2011}, DOI = {10.1007/s00466-011-0571-z} } Abstract:
We present the multiscale space-time techniques we have developed for fluid-structure interaction (FSI) computations. Some of these techniques are multiscale in the way the time integration is performed (i.e. temporally multiscale), some are multiscale in the way the spatial discretization is done (i.e. spatially multiscale), and some are in the context of the sequentially-coupled FSI (SCFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling T AFSM . In the multiscale SCFSI technique, the FSI computational effort is reduced at the stage we do not need it and the accuracy of the fluid mechanics (or structural mechanics) computation is increased at the stage we need accurate, detailed flow (or structure) computation. As ways of increasing the computational accuracy when or where needed, and beyond just increasing the mesh refinement or decreasing the time-step size, we propose switching to more accurate versions of the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, using more polynomial power for the basis functions of the spatial discretization or time integration, and using an advanced turbulence model. Specifically, for more polynomial power in time integration, we propose to use NURBS, and as an advanced turbulence model to be used with the DSD/SST formulation, we introduce a space-time version of the residual-based variational multiscale method. We present a number of test computations showing the performance of the multiscale space-time techniques we are proposing. We also present a stability and accuracy analysis for the higher-accuracy versions of the DSD/SST formulation. © 2011 Springer-Verlag.

[169]

T.E. Tezduyar, K. Takizawa, T. Brummer, and P.R. Chen, “Space–time fluid–structure interaction modeling of patient-specific cerebral aneurysms”, International Journal for Numerical Methods in Biomedical Engineering, 27 (2011) 1665–1710, 10.1002/cnm.1433
@ARTICLE{Tezduyar10b, AUTHOR = {T. E.~Tezduyar and K.~Takizawa and T.~Brummer and P. R.~Chen}, PAGES = {1665--1710}, JOURNAL = {International Journal for Numerical Methods in Biomedical Engineering}, VOLUME = {27}, TITLE = {Space--Time Fluid--Structure Interaction Modeling of Patient-Specific Cerebral Aneurysms}, YEAR = {2011}, DOI = {10.1002/cnm.1433} } Abstract:
We provide an extensive overview of the core and special techniques developed earlier by the Team for Advanced Flow Simulation and Modeling (T{black star}AFSM) for space-time fluid-structure interaction (FSI) modeling of patient-specific cerebral aneurysms. The core FSI techniques are the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation and the stabilized space-time FSI (SSTFSI) technique. The special techniques include techniques for calculating an estimated zero-pressure (EZP) arterial geometry, a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape, techniques for using variable arterial wall thickness, mesh generation techniques for building layers of refined fluid mechanics mesh near the arterial walls, a recipe for pre-FSI computations that improve the convergence of the FSI computations, the Sequentially-Coupled Arterial FSI (SCAFSI) technique and its multiscale versions, techniques for the projection of fluid-structure interface stresses, calculation of the wall shear stress (WSS) and calculation of the oscillatory shear index (OSI) and arterial-surface extraction and boundary condition techniques. We show how these techniques work with results from earlier computations. We also describe the arterial FSI techniques developed and implemented recently by the T{black star}AFSM and present a sample from a wide set of patient-specific cerebral-aneurysm models we computed recently. © 2011 John Wiley & Sons, Ltd.

[168]

S. Takase, K. Kashiyama, S. Tanaka, and T.E. Tezduyar, “Space–time SUPG formulation of the shallow-water equations”, International Journal for Numerical Methods in Fluids, 64 (2010) 1379–1394, 10.1002/fld.2464
@ARTICLE{Kashiyama10a, AUTHOR = {S.~Takase and K.~Kashiyama and S.~Tanaka and T. E.~Tezduyar}, PAGES = {1379--1394}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {64}, TITLE = {Space--Time {SUPG} Formulation of the Shallow-Water Equations}, YEAR = {2010}, DOI = {10.1002/fld.2464} } Abstract:
We present a new space-time SUPG formulation of the shallow-water equations. In this formulation, we use a stabilization parameter that was introduced for compressible flows and a new shock-capturing parameter. In the context of two test problems, we evaluate the performance of the new shock-capturing parameter. We also evaluate the performance of the space-time SUPG formulation compared to the semi-discrete SUPG formulation, where the system of semi-discrete equations is solved with the central-difference (Crank-Nicolson) time-integration algorithm. © 2010 John Wiley & Sons, Ltd.

[167]

A. Corsini, F. Rispoli, and T.E. Tezduyar, “Stabilized finite element computation of NOx emission in aero-engine combustors”, International Journal for Numerical Methods in Fluids, 65 (2011) 254–270, 10.1002/fld.2451
@ARTICLE{Corsini10a, AUTHOR = {A.~Corsini and F.~Rispoli and T. E.~Tezduyar}, PAGES = {254--270}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {Stabilized Finite Element Computation of {NO}x Emission in Aero-engine Combustors}, YEAR = {2011}, DOI = {10.1002/fld.2451} } Abstract:
A stabilized finite element formulation for the computation of turbulent reacting flows and NOx emission is presented. The method is based on the Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulations, complemented with directionally formulated diffusion for reaction-dominated flows ('DRDJ' stabilization). The stabilized formulation is applied to the advection-diffusion-reaction equations governing the turbulent combustion and the NOx emission equations based on the thermal and the N2O pathways. The simulation is carried out for a co-axial burner, with a non-premixed swirling flame. The burner is operated at high pressure to represent the take-off conditions for an aero-engine. The vortical patterns of the swirling flame are analyzed together with the temperature field and flame position. The NOx formation processes are discussed, providing insight into the features of thermal and N2O mechanisms. © 2010 John Wiley & Sons, Ltd.

[166]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Influencing factors in image-based fluid–structure interaction computation of cerebral aneurysms”, International Journal for Numerical Methods in Fluids, 65 (2011) 324–340, 10.1002/fld.2448
@ARTICLE{Torii10a, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {324--340}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {Influencing Factors in Image-Based Fluid--Structure Interaction Computation of Cerebral Aneurysms}, YEAR = {2011}, DOI = {10.1002/fld.2448} } Abstract:
We review and summarize our research activities in fluid-structure interaction (FSI) analysis of cerebral aneurysms using anatomically realistic geometry models based on medical images. Emphasis is placed on influencing factors in computational FSI, and their role and clinical implications are discussed in terms of the wall shear stress (WSS). The key factors are: (1) arterial and aneurysm geometries, (2) wall structure modeling, (3) blood pressure, (4) outflow conditions and (5) inflow conditions. Among these, we find the impact of the arterial and aneurysm geometries to be the most significant. Blood pressure also has a significant impact on the WSS distribution; a hypothetical hypertensive blood pressure condition could help estimate the rupture risk for an aneurysm. We find the other three factors to be minor compared with the arterial and aneurysm geometries and blood pressure, although the level of influence could be unique to the middle cerebral artery aneurysms that we have been focusing on in our studies. © 2010 John Wiley & Sons, Ltd.

[165]

M. Manguoglu, K. Takizawa, A.H. Sameh, and T.E. Tezduyar, “Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement”, International Journal for Numerical Methods in Fluids, 65 (2011) 135–149, 10.1002/fld.2415
@ARTICLE{Manguoglu10a, AUTHOR = {M.~Manguoglu and K.~Takizawa and A. H.~Sameh and T. E.~Tezduyar}, PAGES = {135--149}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {Nested and Parallel Sparse Algorithms for Arterial Fluid Mechanics Computations with Boundary Layer Mesh Refinement}, YEAR = {2011}, DOI = {10.1002/fld.2415} } Abstract:
Arterial fluid-structure interaction (FSI) computations involve a number of numerical challenges. Because blood flow is incompressible, iterative solution of the fluid mechanics part of the linear equation system at every nonlinear iteration of each time step is one of those challenges, especially for computations over slender domains and in the presence of boundary layer mesh refinement. In this paper we address that challenge. As test cases, we use equation systems from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm, with thin layers of elements near the arterial wall. We show how the preconditioning techniques, we propose for solving these large sparse nonsymmetric systems, perform at different time steps of the computation over a cardiac cycle. We also present a new hybrid parallel sparse linear system solver 'DD-Spike' and demonstrate its scalability. © 2010 John Wiley & Sons, Ltd.

[164]

T.E. Tezduyar, “Comment on ‘Three-dimensional aerodynamic simulations of jumping paratroopers and falling cargo payloads’”, Journal of Aircraft, 48 (2011) 1471–1472, 10.2514/1.C000186
@ARTICLE{Tezduyar10a, AUTHOR = {T. E.~Tezduyar}, PAGES = {1471--1472}, JOURNAL = {Journal of Aircraft}, VOLUME = {48}, TITLE = {Comment on `{T}hree-Dimensional Aerodynamic Simulations of Jumping Paratroopers and Falling Cargo Payloads'}, YEAR = {2011}, DOI = {10.2514/1.C000186} }

[163]

Y. Bazilevs, M.-C. Hsu, I. Akkerman, S. Wright, K. Takizawa, B. Henicke, T. Spielman, and T.E. Tezduyar, “3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics”, International Journal for Numerical Methods in Fluids, 65 (2011) 207–235, 10.1002/fld.2400
@ARTICLE{Bazilevs10a, AUTHOR = {Y.~Bazilevs and Ming-Chen Hsu and I.~Akkerman and S.~Wright and K.~Takizawa and B.~Henicke and T.~Spielman and T. E.~Tezduyar}, PAGES = {207--235}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {3{D} Simulation of Wind Turbine Rotors at Full Scale. {P}art {I}: {G}eometry Modeling and Aerodynamics}, YEAR = {2011}, DOI = {10.1002/fld.2400} } Abstract:
In this two-part paper we present a collection of numerical methods combined into a single framework, which has the potential for a successful application to wind turbine rotor modeling and simulation. In Part 1 of this paper we focus on: 1. The basics of geometry modeling and analysis-suitable geometry construction for wind turbine rotors; 2. The fluid mechanics formulation and its suitability and accuracy for rotating turbulent flows; 3. The coupling of air flow and a rotating rigid body. In Part 2 we focus on the structural discretization for wind turbine blades and the details of the fluid-structure interaction computational procedures. The methods developed are applied to the simulation of the NREL 5MW offshore baseline wind turbine rotor. The simulations are performed at realistic wind velocity and rotor speed conditions and at full spatial scale. Validation against published data is presented and possibilities of the newly developed computational framework are illustrated on several examples. © 2010 John Wiley & Sons, Ltd.

[162]

K. Takizawa, S. Wright, C. Moorman, and T.E. Tezduyar, “Fluid–structure interaction modeling of parachute clusters”, International Journal for Numerical Methods in Fluids, 65 (2011) 286–307, 10.1002/fld.2359
@ARTICLE{Takizawa10a, AUTHOR = {K.~Takizawa and S.~Wright and C.~Moorman and T. E.~Tezduyar}, PAGES = {286--307}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {Fluid--Structure Interaction Modeling of Parachute Clusters}, YEAR = {2011}, DOI = {10.1002/fld.2359} } Abstract:
We address some of the computational challenges involved in fluid-structure interaction (FSI) modeling of clusters of ringsail parachutes. The geometric complexity created by the construction of the parachute from 'rings' and 'sails' with hundreds of gaps and slits makes this class of FSI modeling inherently challenging. There is still much room for advancing the computational technology for FSI modeling of a single raingsail parachute, such as improving the Homogenized Modeling of Geometric Porosity (HMGP) and developing special techniques for computing the reefed stages of the parachute and its disreefing. While we continue working on that, we are also developing special techniques targeting cluster modeling, so that the computational technology goes beyond the single parachute and the challenges specific to parachute clusters are addressed. The rotational-periodicity technique we describe here is one of such special techniques, and we use that for computing good starting conditions for FSI modeling of parachute clusters. In addition to reporting our preliminary FSI computations for parachute clusters, we present results from those starting-condition computations. In the category of more fundamental computational technologies, we discuss how we are improving the HMGP by increasing the resolution of the fluid mechanics mesh used in the HMGP computation and also by increasing the number of gores used. Also in that category, we describe how we use the multiscale sequentially coupled FSI techniques to improve the accuracy in computing the structural stresses in parts of the structure where we want to report more accurate values. All these special techniques are used in conjunction with the Stabilized Space-Time Fluid-Structure Interaction (SSTFSI) technique. Therefore, we also present in this paper a brief stability and accuracy analysis for the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, which is the core numerical technology of the SSTFSI technique. © 2010 John Wiley & Sons, Ltd.

[161]

K. Takizawa, C. Moorman, S. Wright, J. Purdue, T. McPhail, P.R. Chen, J. Warren, and T.E. Tezduyar, “Patient-specific arterial fluid–structure interaction modeling of cerebral aneurysms”, International Journal for Numerical Methods in Fluids, 65 (2011) 308–323, 10.1002/fld.2360
@ARTICLE{Takizawa09f, AUTHOR = {K.~Takizawa and C.~Moorman and S.~Wright and J.~Purdue and T.~McPhail and P. R.~Chen and J.~Warren and T. E.~Tezduyar}, PAGES = {308--323}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {Patient-Specific Arterial Fluid--Structure Interaction Modeling of Cerebral Aneurysms}, YEAR = {2011}, DOI = {10.1002/fld.2360} } Abstract:
We address the computational challenges related to the extraction of the arterial-lumen geometry, mesh generation and starting-point determination in the computation of arterial fluid-structure interactions (FSI) with patient-specific data. The methods we propose here to address those challenges include techniques for constructing suitable cutting planes at the artery inlets and outlets and specifying on those planes proper boundary conditions for the fluid mechanics, structural mechanics and fluid mesh motion and a technique for the improved calculation of an estimated zero-pressure arterial geometry. We use the stabilized space-time FSI technique, together with a number of special techniques recently developed for arterial FSI. We focus on three patient-specific cerebral artery segments with aneurysm, where the lumen geometries are extracted from 3D rotational angiography. © 2010 John Wiley & Sons, Ltd.

[160]

K. Takizawa, C. Moorman, S. Wright, T. Spielman, and T.E. Tezduyar, “Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes”, International Journal for Numerical Methods in Fluids, 65 (2011) 271–285, 10.1002/fld.2348
@ARTICLE{Takizawa09e, AUTHOR = {K.~Takizawa and C.~Moorman and S.~Wright and T.~Spielman and T. E.~Tezduyar}, PAGES = {271--285}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {65}, TITLE = {Fluid--Structure Interaction Modeling and Performance Analysis of the {O}rion Spacecraft Parachutes}, YEAR = {2011}, DOI = {10.1002/fld.2348} } Abstract:
We focus on fluid-structure interaction (FSI) modeling and performance analysis of the ringsail parachutes to be used with the Orion spacecraft. We address the computational challenges with the latest techniques developed by the T-AFSM (Team for Advanced Flow Simulation and Modeling) in conjunction with the SSTFSI (Stabilized Space-Time Fluid-Structure Interaction) technique. The challenges involved in FSI modeling include the geometric porosity of the ringsail parachutes with ring gaps and sail slits. We investigate the performance of three possible design configurations of the parachute canopy. We also describe the techniques developed recently for building a consistent starting condition for the FSI computations, discuss rotational periodicity techniques for improving the geometric-porosity modeling, and introduce a new version of the HMGP (Homogenized Modeling of Geometric Porosity). © 2010 John Wiley & Sons, Ltd.

[159]

T.E. Tezduyar, “Comments on paratrooper-separation modeling with the DSD/SST formulation and FOIST”, International Journal for Numerical Methods in Fluids, 66 (2011) 1068–1072, 10.1002/fld.2299
@ARTICLE{Tezduyar09h, AUTHOR = {T. E.~Tezduyar}, PAGES = {1068--1072}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {66}, TITLE = {Comments on Paratrooper-Separation Modeling with the {DSD/SST} Formulation and {FOIST}}, YEAR = {2011}, DOI = {10.1002/fld.2299} } Abstract:
We provide a brief chronological background on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, its use in aerodynamic modeling of a paratrooper separating from an aircraft, and the fluid-object interactions subcomputation technique (FOIST). © 2010 John Wiley & Sons, Ltd.

[158]

T.E. Tezduyar, “Comments on ‘Adiabatic shock capturing in perfect gas hypersonic flows’”, International Journal for Numerical Methods in Fluids, 66 (2011) 935–938, 10.1002/fld.2293
@ARTICLE{Tezduyar09g, AUTHOR = {T. E.~Tezduyar}, PAGES = {935--938}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {66}, TITLE = {Comments on `{A}diabatic shock capturing in perfect gas hypersonic flows'}, YEAR = {2011}, DOI = {10.1002/fld.2293} } Abstract:
Some comments are provided on the shock-capturing techniques and stabilization parameters used in a recent paper (B.S. Kirk, Int. J. Numer. Meth. Fluids 2009; DOI: 10.1002/fld.2195) in conjunction with the SUPG formulation of compressible flows. © 2010 John Wiley & Sons, Ltd.

[157]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms”, Computational Mechanics, 46 (2010) 43–52, 10.1007/s00466-009-0439-7
@ARTICLE{Torii09c, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {43--52}, JOURNAL = {Computational Mechanics}, VOLUME = {46}, TITLE = {Role of {0D} Peripheral Vasculature Model in Fluid--Structure Interaction Modeling of Aneurysms}, YEAR = {2010}, DOI = {10.1007/s00466-009-0439-7} } Abstract:
Patient-specific simulations based on medical images such as CT and MRI offer information on the hemodynamic and wall tissue stress in patient-specific aneurysm configurations. These are considered important in predicting the rupture risk for individual aneurysms but are not possible to measure directly. In this paper, fluid-structure interaction (FSI) analyses of a cerebral aneurysm at the middle cerebral artery (MCA) bifurcation are presented. A 0D structural recursive tree model of the peripheral vasculature is incorporated and its impedance is coupled with the 3D FSI model to compute the outflow through the two branches accurately. The results are compared with FSI simulation with prescribed pressure variation at the outlets. The comparison shows that the pressure at the two outlets are nearly identical even with the peripheral vasculature model and the flow division to the two branches is nearly the same as what we see in the simulation without the peripheral vasculature model. This suggests that the role of the peripheral vasculature in FSI modeling of the MCA aneurysm is not significant. © 2009 Springer-Verlag.

[156]

T.E. Tezduyar, K. Takizawa, C. Moorman, S. Wright, and J. Christopher, “Space–time finite element computation of complex fluid–structure interactions”, International Journal for Numerical Methods in Fluids, 64 (2010) 1201–1218, 10.1002/fld.2221
@ARTICLE{Tezduyar09f, AUTHOR = {T. E.~Tezduyar and K.~Takizawa and C.~Moorman and S.~Wright and J.~Christopher}, PAGES = {1201--1218}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {64}, TITLE = {Space--Time Finite Element Computation of Complex Fluid--Structure Interactions}, YEAR = {2010}, DOI = {10.1002/fld.2221} } Abstract:
New special fluid-structure interaction (FSI) techniques, supplementing the ones developed earlier, are employed with the Stabilized Space-Time FSI (SSTFSI) technique. The new special techniques include improved ways of calculating the equivalent fabric porosity in Homogenized Modeling of Geometric Porosity (HMGP), improved ways of building a starting point in FSI computations, ways of accounting for fluid forces acting on structural components that are not expected to influence the flow, adaptive HMGP, and multiscale sequentially coupled FSI techniques. While FSI modeling of complex parachutes was the motivation behind developing some of these techniques, they are also applicable to other classes of complex FSI problems. We also present new ideas to increase the scope of our FSI and CFD techniques. © 2009 John Wiley & Sons, Ltd.

[155]

K. Takizawa, C. Moorman, S. Wright, J. Christopher, and T.E. Tezduyar, “Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions”, Computational Mechanics, 46 (2010) 31–41, 10.1007/s00466-009-0425-0
@ARTICLE{Takizawa09d, AUTHOR = {K.~Takizawa and C.~Moorman and S.~Wright and J.~Christopher and T. E.~Tezduyar}, PAGES = {31--41}, JOURNAL = {Computational Mechanics}, VOLUME = {46}, TITLE = {Wall Shear Stress Calculations in Space--Time Finite Element Computation of Arterial Fluid--Structure Interactions}, YEAR = {2010}, DOI = {10.1007/s00466-009-0425-0} } Abstract:
The stabilized space-time fluid-structure interaction (SSTFSI) technique was applied to arterial FSI problems soon after its development by the Team for Advanced Flow Simulation and Modeling. The SSTFSI technique is based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation and is supplemented with a number of special techniques developed for arterial FSI. The special techniques developed in the recent past include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, Sequentially Coupled Arterial FSI technique, using layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at inflow boundaries with non-circular shape. In this paper we introduce some additional special techniques, related to the projection of fluid-structure interface stresses, calculation of the wall shear stress (WSS), and calculation of the oscillatory shear index. In the test computations reported here, we focus on WSS calculations in FSI modeling of a patient-specific middle cerebral artery segment with aneurysm. Two different structural mechanics meshes and three different fluid mechanics meshes are tested to investigate the influence of mesh refinement on the WSS calculations. © 2009 Springer-Verlag.

[154]

T.E. Tezduyar, K. Takizawa, C. Moorman, S. Wright, and J. Christopher, “Multiscale sequentially-coupled arterial FSI technique”, Computational Mechanics, 46 (2010) 17–29, 10.1007/s00466-009-0423-2
@ARTICLE{Tezduyar09e, AUTHOR = {T. E.~Tezduyar and K.~Takizawa and C.~Moorman and S.~Wright and J.~Christopher}, PAGES = {17--29}, JOURNAL = {Computational Mechanics}, VOLUME = {46}, TITLE = {Multiscale Sequentially-Coupled Arterial {FSI} Technique}, YEAR = {2010}, DOI = {10.1007/s00466-009-0423-2} } Abstract:
Multiscale versions of the Sequentially-Coupled Arterial Fluid-Structure Interaction (SCAFSI) technique are presented. The SCAFSI technique was introduced as an approximate FSI approach in arterial fluid mechanics. It is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. First we compute a "reference" arterial deformation as a function of time, driven only by the blood pressure profile of the cardiac cycle. Then we compute a sequence of updates involving mesh motion, fluid dynamics calculations, and recomputing the arterial deformation. The SCAFSI technique was developed and tested in conjunction with the stabilized space-time FSI (SSTFSI) technique. Beyond providing a computationally more economical alternative to the fully coupled arterial FSI approach, the SCAFSI technique brings additional flexibility, such as being able to carry out the computations in a spatially or temporally multiscale fashion. In the test computations reported here for the spatially multiscale versions of the SCAFSI technique, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. The arterial structure is modeled with the continuum element made of hyperelastic (Fung) material. © 2009 Springer-Verlag.

[153]

M. Manguoglu, K. Takizawa, A.H. Sameh, and T.E. Tezduyar, “Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement”, Computational Mechanics, 46 (2010) 83–89, 10.1007/s00466-009-0426-z
@ARTICLE{Manguoglu09a, AUTHOR = {M.~Manguoglu and K.~Takizawa and A. H.~Sameh and T. E.~Tezduyar}, PAGES = {83--89}, JOURNAL = {Computational Mechanics}, VOLUME = {46}, TITLE = {Solution of Linear Systems in Arterial Fluid Mechanics Computations with Boundary Layer Mesh Refinement}, YEAR = {2010}, DOI = {10.1007/s00466-009-0426-z} } Abstract:
Computation of incompressible flows in arterial fluid mechanics, especially because it involves fluid-structure interaction, poses significant numerical challenges. Iterative solution of the fluid mechanics part of the equation systems involved is one of those challenges, and we address that in this paper, with the added complication of having boundary layer mesh refinement with thin layers of elements near the arterial wall. As test case, we use matrix data from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm. It is well known that solving linear systems that arise in incompressible flow computations consume most of the time required by such simulations. For solving these large sparse nonsymmetric systems, we present effective preconditioning techniques appropriate for different stages of the computation over a cardiac cycle. © 2009 Springer-Verlag.

[152]

A. Corsini, C. Iossa, F. Rispoli, and T.E. Tezduyar, “A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors”, Computational Mechanics, 46 (2010) 159–167, 10.1007/s00466-009-0441-0
@ARTICLE{Corsini09a, AUTHOR = {A.~Corsini and C.~Iossa and F.~Rispoli and T. E.~Tezduyar}, PAGES = {159--167}, JOURNAL = {Computational Mechanics}, VOLUME = {46}, TITLE = {A {DRD} Finite Element Formulation for Computing Turbulent Reacting Flows in Gas Turbine Combustors}, YEAR = {2010}, DOI = {10.1007/s00466-009-0441-0} } Abstract:
An effective multiscale treatment of turbulent reacting flows is presented with the use of a stabilized finite element formulation. The method proposed is developed based on the streamline-upwind/Petrov-Galerkin (SUPG) formulation, and includes discontinuity capturing in the form of a new generation "DRD" method, namely the "DRDJ" technique. The stabilized formulation is applied to finite-rate chemistry modelling based on mixture-fraction approaches with the so-called presumed-PDF technique. The turbulent combustion process is simulated for an aero-engine combustor configuration of RQL concept in non-premixed flame regime. The comparative analysis of the temperature and velocity fields demonstrate that the proposed SUPG+DRDJ formulation outperforms the stand-alone SUPG method. The improved accuracy is demonstrated in terms of the combustor overall performance, and the mechanisms involved in the distribution of the numerical diffusivity are also discussed. © 2009 Springer-Verlag.

[151]

T.E. Tezduyar, “Comments on ‘Simplex space-time meshes in finite element simulations’”, International Journal for Numerical Methods in Fluids, 60 (2009) 1289–1290, 10.1002/fld.1933
@ARTICLE{Tezduyar09d2, AUTHOR = {T. E.~Tezduyar}, PAGES = {1289--1290}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {60}, TITLE = {Comments on `{S}implex space-time meshes in finite element simulations'}, YEAR = {2009}, DOI = {10.1002/fld.1933} } Abstract:
Some comments are provided on the citations offered in a recent paper (M. Behr, Int. J. Numer. Meth. Fluids 2008; 57:1421-1434) that describes space-time finite element computations of advection of 'Gaussian hills', including computations with mesh refinement in the time direction. Copyright © 2008 John Wiley & Sons, Ltd.

[150]

T.E. Tezduyar, “Correct implementation of the Fluid–Object Interactions Subcomputation Technique (FOIST)”, Communications in Numerical Methods in Engineering, 25 (2009) 1055–1058, 10.1002/cnm.1312
@ARTICLE{Tezduyar09d, AUTHOR = {T. E.~Tezduyar}, PAGES = {1055--1058}, JOURNAL = {Communications in Numerical Methods in Engineering}, VOLUME = {25}, TITLE = {Correct Implementation of the {F}luid--{O}bject {I}nteractions {S}ubcomputation {T}echnique ({FOIST})}, YEAR = {2009}, DOI = {10.1002/cnm.1312} } Abstract:
Full understanding of the fluid-object interactions subcomputation technique (FOIST) and the related fundamental concepts in dynamics and fluid mechanics is essential in using this technique in a meaningful way. We explain what constitutes a correct implementation of the FOIST and give a published example of what does not. Copyright © 2009 John Wiley & Sons, Ltd.

[149]

M.-C. Hsu, Y. Bazilevs, V.M. Calo, T.E. Tezduyar, and T.J.R. Hughes, “Improving stability of stabilized and multiscale formulations in flow simulations at small time steps”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 828–840, 10.1016/j.cma.2009.06.019
@ARTICLE{Hsu09a, AUTHOR = {Ming-Chen Hsu and Y.~Bazilevs and V. M.~Calo and T. E.~Tezduyar and T. J. R.~Hughes}, PAGES = {828--840}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {199}, TITLE = {Improving Stability of Stabilized and Multiscale Formulations in Flow Simulations at Small Time Steps}, YEAR = {2010}, DOI = {10.1016/j.cma.2009.06.019} } Abstract:
The objective of this paper is to show that use of the element-vector-based definition of stabilization parameters, introduced in [T.E. Tezduyar, Computation of moving boundaries and interfaces and stabilization parameters, Int. J. Numer. Methods Fluids 43 (2003) 555-575; T.E. Tezduyar, Y. Osawa, Finite element stabilization parameters computed from element matrices and vectors, Comput. Methods Appl. Mech. Engrg. 190 (2000) 411-430], circumvents the well-known instability associated with conventional stabilized formulations at small time steps. We describe formulations for linear advection-diffusion and incompressible Navier-Stokes equations and test them on three benchmark problems: advection of an L-shaped discontinuity, laminar flow in a square domain at low Reynolds number, and turbulent channel flow at friction-velocity Reynolds number of 395. © 2009 Elsevier B.V. All rights reserved.

[148]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms”, International Journal for Numerical Methods in Biomedical Engineering, 26 (2010) 336–347, 10.1002/cnm.1289
@ARTICLE{Torii09a, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {336--347}, JOURNAL = {International Journal for Numerical Methods in Biomedical Engineering}, VOLUME = {26}, TITLE = {Influence of Wall Thickness on Fluid--Structure Interaction Computations of Cerebral Aneurysms}, YEAR = {2010}, DOI = {10.1002/cnm.1289} } Abstract:
Fluid-structure interaction (FSI) analyses of cerebral aneurysm using patient-specific geometry with uniform and pathological aneurysmal wall thickness models are carried out. The objective is to assess the influence of the wall thickness on the FSI and hemodynamics in aneurysms. Two aneurysm models that were reconstructured based on CT images are used. The arterial wall thickness is set to 0.3mm for the non-aneurysmal artery and to 0.05mm for the aneurysmal wall based on experimental findings. Another set of aneurysm models with a uniform wall thickness of 0.3mm for the entire model is used for comparison. The FSI simulations are carried out using the deforming-spatial-domain/stabilized space-time method with physiological inflow and pressure profiles. Computations with different aneurysmal wall thicknesses depict considerable differences in displacement, flow velocity and wall shear stress (WSS). The wall displacement for the pathological wall model is 61% larger than that of the uniform wall model. Consequently, the flow velocities in the aneurysm with the pathological wall model are lower, and that results in a 51% reduction in WSS on the aneurismal wall. Because low WSS on the aneurymal wall is linked to growth and rupture risk of aneurysm, the results suggest that using uniform wall thickness for the aneurysmal wall could underestimate risk in aneurysms. Copyright © 2009 John Wiley & Sons, Ltd.

[147]

K. Takizawa, J. Christopher, T.E. Tezduyar, and S. Sathe, “Space–time finite element computation of arterial fluid–structure interactions with patient-specific data”, International Journal for Numerical Methods in Biomedical Engineering, 26 (2010) 101–116, 10.1002/cnm.1241
@ARTICLE{Takizawa09a, AUTHOR = {K.~Takizawa and J.~Christopher and T. E.~Tezduyar and S.~Sathe}, PAGES = {101--116}, JOURNAL = {International Journal for Numerical Methods in Biomedical Engineering}, VOLUME = {26}, TITLE = {Space--Time Finite Element Computation of Arterial Fluid--Structure Interactions with Patient-Specific Data}, YEAR = {2010}, DOI = {10.1002/cnm.1241} } Abstract:
The stabilized space-time fluid-structure interaction (SSTFSI) technique developed by the team for advanced flow simulation and modeling is applied to the computation of arterial fluid-structure interaction (FSI) with patient-specific data. The SSTFSI technique is based on the deforming-spatial-domain/stabilized space-time formulation and is supplemented with a number of special techniques developed for arterial FSI. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape. In the test computations reported here, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. Copyright © 2009 John Wiley & Sons, Ltd.

[146]

L. Catabriga, D.A.F.de Souza, A.L.G.A. Coutinho, and T.E. Tezduyar, “Three-dimensional edge-based SUPG computation of inviscid compressible flows with YZβ shock-capturing”, Journal of Applied Mechanics, 76 (2009) 021208, 10.1115/1.3062968
@ARTICLE{Catabriga08a, AUTHOR = {L.~Catabriga and D. A. F.~de Souza and A. L. G. A.~Coutinho and T. E.~Tezduyar}, PAGES = {021208}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {76}, TITLE = {Three-Dimensional Edge-Based {SUPG} Computation of Inviscid Compressible Flows with {YZ}$\beta$ Shock-Capturing}, YEAR = {2009}, DOI = {10.1115/1.3062968} } Abstract:
The streamline-upwind/Petrov-Galerkin (SUPG) formulation of compressible flows based on conservation variables, supplemented with shock-capturing, has been successfully used over a quarter of a century. In this paper, for inviscid compressible flows, the YZβ shock-capturing parameter, which was developed recently and is based on conservation variables only, is compared with an earlier parameter derived based on the entropy variables. Our studies include comparing, in the context of these two versions of the SUPG formulation, computational efficiency of the element- and edge-based data structures in iterative computation of compressible flows. Tests include 1D, 2D, and 3D examples. Copyright © 2009 by ASME.

[145]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Fluid–structure interaction modeling of blood flow and cerebral aneurysm: Significance of artery and aneurysm shapes”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3613–3621, 10.1016/j.cma.2008.08.020
@ARTICLE{Torii08b, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {3613--3621}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {198}, TITLE = {Fluid--Structure Interaction Modeling of Blood Flow and Cerebral Aneurysm: {S}ignificance of Artery and Aneurysm Shapes}, YEAR = {2009}, DOI = {10.1016/j.cma.2008.08.020} } Abstract:
Because wall shear stress (WSS) is known to play an important role in initiation, growth and rupture of cerebral aneurysm, predicting the hemodynamic forces near the aneurysmal site helps with understanding aneurysms better. Earlier research reports indicate that the WSS around the aneurysmal site has a significant relationship with the vascular and aneurysm morphology. It was also shown statistically that the aneurysm shape (aspect ratio) is an indicator of rupture risk in cerebral aneurysm. In this study, fluid-structure interaction (FSI) modeling of a ruptured aneurysm, two unruptured aneurysms at the middle cerebral artery (MCA) bifurcation, and a MCA bifurcation without aneurysm is carried out using vascular geometries reconstructed from CT images. We use pulsatile boundary conditions based on a physiological flow velocity waveform and investigate the relationship between the hemodynamic forces and vascular morphology for different arteries and aneurysms. The results are compared with the results obtained for the rigid arterial wall to highlight the role of FSI in the patient-specific modeling of cerebral aneurysm. The results show that the interaction between the blood flow and arterial deformation alters the hemodynamic forces acting on the arterial wall and the interaction strongly depends on the individual aneurysm shapes. Flow impingement on the arterial wall plays a key role in determining the interaction and hemodynamic forces. When the blood flow impinges strongly on the wall, the maximum WSS tends to decrease due to the flow-wall interaction. When the blood flows straight into an aneurysm, the flow and the resulting WSS patterns are altered both qualitatively and quantitatively. When the blood in the aneurysm is nearly stagnant, a slow flow is induced by the wall motion, which raises the minimum WSS on the aneurysmal wall. The results reinforce the importance of FSI in patient-specific analysis of cerebral aneurysms. © 2008 Elsevier B.V. All rights reserved.

[144]

A. Corsini, C. Menichini, F. Rispoli, A. Santoriello, and T.E. Tezduyar, “A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms”, Journal of Applied Mechanics, 76 (2009) 021211, 10.1115/1.3062967
@ARTICLE{Corsini08a, AUTHOR = {A.~Corsini and C.~Menichini and F.~Rispoli and A.~Santoriello and T. E.~Tezduyar}, PAGES = {021211}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {76}, TITLE = {A Multiscale Finite Element Formulation with Discontinuity Capturing for Turbulence Models with Dominant Reactionlike Terms}, YEAR = {2009}, DOI = {10.1115/1.3062967} } Abstract:
A stabilization technique targeting the Reynolds-averaged Navier-Stokes (RANS) equations is proposed to account for the multiscale nature of turbulence and high solution gradients. The objective is effective stabilization in computations with the advectiondiffusion reaction equations, which are typical of the class of turbulence scaledetermining equations where reaction-dominated effects strongly influence the boundary layer prediction in the presence of nonequilibrium phenomena. The stabilization technique, which is based on a variational multiscale method, includes a discontinuitycapturing term designed to be operative when the solution gradients are high and the reactionlike terms are dominant. As test problems, we use a 2D model problem and 3D flow computation for a linear compressor cascade. Copyright © 2009 by ASME.

[143]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: Influence of structural modeling”, Computational Mechanics, 43 (2008) 151–159, 10.1007/s00466-008-0325-8
@ARTICLE{Torii08a, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {151--159}, JOURNAL = {Computational Mechanics}, VOLUME = {43}, TITLE = {Fluid--Structure Interaction Modeling of a Patient-Specific Cerebral Aneurysm: {I}nfluence of Structural Modeling}, YEAR = {2008}, DOI = {10.1007/s00466-008-0325-8} } Abstract:
Fluid-structure interaction (FSI) simulations of a cerebral aneurysm with the linearly elastic and hyper-elastic wall constitutive models are carried out to investigate the influence of the wall-structure model on patient-specific FSI simulations. The maximum displacement computed with the hyper-elastic model is 36% smaller compared to the linearly elastic material model, but the displacement patterns such as the site of local maxima are not sensitive to the wall models. The blood near the apex of an aneurysm is likely to be stagnant, which causes very low wall shear stress and is a factor in rupture by degrading the aneurysmal wall. In this study, however, relatively high flow velocities due to the interaction between the blood flow and aneurysmal wall are seen to be independent of the wall model. The present results indicate that both linearly elastic and hyper-elastic models can be useful to investigate aneurysm FSI. © 2008 Springer-Verlag.

[142]

M.A. Cruchaga, D.J. Celentano, and T.E. Tezduyar, “Computational modeling of the collapse of a liquid column over an obstacle and experimental validation”, Journal of Applied Mechanics, 76 (2009) 021202, 10.1115/1.3057439
@ARTICLE{Cruchaga08a, AUTHOR = {M. A.~Cruchaga and D. J.~Celentano and T. E.~Tezduyar}, PAGES = {021202}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {76}, TITLE = {Computational Modeling of the Collapse of a Liquid Column Over an Obstacle and Experimental Validation}, YEAR = {2009}, DOI = {10.1115/1.3057439} } Abstract:
We present the numerical and experimental analyses of the collapse of a water column over an obstacle. The physical model consists of a water column initially confined by a closed gate inside a glass box. An obstacle is placed between the gate and the right wall of the box, inside the initially unfilled zone. Once the gate is opened, the liquid spreads in the container and over the obstacle. Measurements of the liquid height along the walls and a middle control section are obtained from videos. The computational modeling is carried out using a moving interface technique, namely, the edge-tracked interface locator technique, to calculate the evolution of the water-air interface. The analysis involves a water-column aspect ratio of 2, with different obstacle geometries. The numerical predictions agree reasonably well with the experimental trends. Copyright © 2009 by ASME.

[141]

T.J.R. Hughes, G. Scovazzi, and T.E. Tezduyar, “Stabilized methods for compressible flows”, Journal of Scientific Computing, 43 (2010) 343–368, 10.1007/s10915-008-9233-5
@ARTICLE{Hughes08a, AUTHOR = {T. J. R.~Hughes and G.~Scovazzi and T. E.~Tezduyar}, PAGES = {343--368}, JOURNAL = {Journal of Scientific Computing}, VOLUME = {43}, TITLE = {Stabilized Methods for Compressible Flows}, YEAR = {2010}, DOI = {10.1007/s10915-008-9233-5} } Abstract:
This article reviews 25 years of research of the authors and their collaborators on stabilized methods for compressible flow computations. An historical perspective is adopted to document the main advances from the initial developments to modern approaches. © 2008 Springer Science+Business Media, LLC.

[140]

M. Manguoglu, A.H. Sameh, F. Saied, T.E. Tezduyar, and S. Sathe, “Preconditioning techniques for nonsymmetric linear systems in the computation of incompressible flows”, Journal of Applied Mechanics, 76 (2009) 021204, 10.1115/1.3059576
@ARTICLE{Manguoglu08b, AUTHOR = {M.~Manguoglu and A. H.~Sameh and F.~Saied and T. E.~Tezduyar and S.~Sathe}, PAGES = {021204}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {76}, TITLE = {Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows}, YEAR = {2009}, DOI = {10.1115/1.3059576} } Abstract:
In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier-Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously. Copyright © 2009 by ASME.

[139]

F. Rispoli, R. Saavedra, F. Menichini, and T.E. Tezduyar, “Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZβ shock-capturing”, Journal of Applied Mechanics, 76 (2009) 021209, 10.1115/1.3057496
@ARTICLE{Rispoli08a, AUTHOR = {F.~Rispoli and R.~Saavedra and F.~Menichini and T. E.~Tezduyar}, PAGES = {021209}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {76}, TITLE = {Computation of Inviscid Supersonic Flows around Cylinders and Spheres with the {V-SGS} Stabilization and {YZ}$\beta$ Shock-Capturing}, YEAR = {2009}, DOI = {10.1115/1.3057496} } Abstract:
The YZβ shock-capturing technique was introduced originally for use in combination with the streamline-upwind/Petrov-Galerkin (SUPG) formulation of compressible flows in conservation variables. It is a simple residual-based shock-capturing technique. Later it was also combined with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables and tested on standard 2D test problems. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. In this paper, we carry out numerical experiments with inviscid supersonic flows around cylinders and spheres to evaluate the performance of the YZβ shock-capturing combined with the V-SGS method. The cylinder computations are carried out at Mach numbers 3 and 8, and the sphere computations are carried out at Mach number 3. The results compare well to those obtained with the YZβ shockcapturing combined with the SUPG formulation, which were shown earlier to compare very favorably to those obtained with the well established OVERFLOW code. Copyright © 2009 by ASME.

[138]

M. Manguoglu, A.H. Sameh, T.E. Tezduyar, and S. Sathe, “A nested iterative scheme for computation of incompressible flows in long domains”, Computational Mechanics, 43 (2008) 73–80, 10.1007/s00466-008-0276-0
@ARTICLE{Manguoglu08a, AUTHOR = {M.~Manguoglu and A. H.~Sameh and T. E.~Tezduyar and S.~Sathe}, PAGES = {73--80}, JOURNAL = {Computational Mechanics}, VOLUME = {43}, TITLE = {A nested iterative scheme for computation of incompressible flows in long domains}, YEAR = {2008}, DOI = {10.1007/s00466-008-0276-0} } Abstract:
We present an effective preconditioning technique for solving the nonsymmetric linear systems encountered in computation of incompressible flows in long domains. The application category we focus on is arterial fluid mechanics. These linear systems are solved using a nested iterative scheme with an outer Richardson scheme and an inner iteration that is handled via a Krylov subspace method. Test computations that demonstrate the robustness of our nested scheme are presented. © 2008 Springer-Verlag.

[137]

T.E. Tezduyar, M. Schwaab, and S. Sathe, “Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) technique”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3524–3533, 10.1016/j.cma.2008.05.024
@ARTICLE{Tezduyar08c, AUTHOR = {T. E.~Tezduyar and M.~Schwaab and S.~Sathe}, PAGES = {3524--3533}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {198}, TITLE = {Sequentially-{C}oupled {A}rterial {F}luid--{S}tructure {I}nteraction ({SCAFSI}) technique}, YEAR = {2009}, DOI = {10.1016/j.cma.2008.05.024} } Abstract:
The Sequentially-Coupled Arterial Fluid-Structure Interaction (SCAFSI) technique is one of the special techniques developed recently by the Team for Advanced Flow Simulation and Modeling (T{star, open}AFSM) for FSI modeling of blood flow and arterial dynamics. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. In the SCAFSI, first we compute a "reference" arterial deformation as a function of time, driven only by the blood pressure profile of the cardiac cycle. Then we compute a sequence of updates involving mesh motion, fluid dynamics calculations, and recomputing the arterial deformation. Although the SCAFSI technique was developed and tested in conjunction with the stabilized space-time FSI (SSTFSI) technique, it can also be used in conjunction with other FSI modeling techniques categorized as moving-mesh methods. The SSTFSI technique is based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation and includes the enhancements introduced recently by the T{star, open}AFSM. The arterial structures can be modeled with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element can be made of linearly-elastic or hyperelastic material (Mooney-Rivlin or Fung). Here we provide an overview of the SCAFSI technique and present a number of test computations for abdominal aortic and cerebral aneurysms, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data. © 2008 Elsevier B.V. All rights reserved.

[136]

S. Sathe and T.E. Tezduyar, “Modeling of fluid–structure interactions with the space–time finite elements: Contact problems”, Computational Mechanics, 43 (2008) 51–60, 10.1007/s00466-008-0299-6
@ARTICLE{Sathe08a, AUTHOR = {S.~Sathe and T. E.~Tezduyar}, PAGES = {51--60}, JOURNAL = {Computational Mechanics}, VOLUME = {43}, TITLE = {Modeling of Fluid--Structure Interactions with the Space--Time Finite Elements: {C}ontact Problems}, YEAR = {2008}, DOI = {10.1007/s00466-008-0299-6} } Abstract:
Fluid-structure interaction computations based on interface-tracking (moving-mesh) techniques are often hindered if the structural surfaces come in contact with each other. As the distance between two structural surfaces tends to zero, the fluid mesh in between distorts severely and eventually becomes invalid. Our objective is to develop a technique for modeling problems where the contacting structural surfaces would otherwise inhibit flow modeling or even fluid-mesh update. In this paper, we present our contact tracking technique that detects impending contact and maintains a minimum distance between the contacting structural surfaces. Our Surface-Edge-Node Contact Tracking (SENCT) technique conducts a topologically hierarchical search to detect contact between each node and the elements ("surfaces"), edges and other nodes. To keep the contacting surfaces apart by a small distance, we apply to the contacted nodes penalty forces in SENCT-Force (SENCT-F) and displacement restrictions in SENCT-Displacement (SENCT-D). By keeping a minimum distance between the contacting surfaces, we are able to update the fluid mesh in between and model the flow accurately. © 2008 Springer-Verlag.

[135]

T.E. Tezduyar, S. Sathe, M. Schwaab, J. Pausewang, J. Christopher, and J. Crabtree, “Fluid–structure interaction modeling of ringsail parachutes”, Computational Mechanics, 43 (2008) 133–142, 10.1007/s00466-008-0260-8
@ARTICLE{Tezduyar08b, AUTHOR = {T. E.~Tezduyar and S.~Sathe and M.~Schwaab and J.~Pausewang and J.~Christopher and J.~Crabtree}, PAGES = {133--142}, JOURNAL = {Computational Mechanics}, VOLUME = {43}, TITLE = {Fluid--structure interaction modeling of ringsail parachutes}, YEAR = {2008}, DOI = {10.1007/s00466-008-0260-8} } Abstract:
In this paper, we focus on fluid-structure interaction (FSI) modeling of ringsail parachutes, where the geometric complexity created by the "rings" and "sails" used in the construction of the parachute canopy poses a significant computational challenge. It is expected that NASA will be using a cluster of three ringsail parachutes, referred to as the "mains", during the terminal descent of the Orion space vehicle. Our FSI modeling of ringsail parachutes is based on the stabilized space-time FSI (SSTFSI) technique and the interface projection techniques that address the computational challenges posed by the geometric complexities of the fluid-structure interface. Two of these interface projection techniques are the FSI Geometric Smoothing Technique and the Homogenized Modeling of Geometric Porosity. We describe the details of how we use these two supplementary techniques in FSI modeling of ringsail parachutes. In the simulations we report here, we consider a single main parachute, carrying one third of the total weight of the space vehicle. We present results from FSI modeling of offloading, which includes as a special case dropping the heat shield, and drifting under the influence of side winds. © 2008 Springer-Verlag.

[134]

T.E. Tezduyar, S. Sathe, J. Pausewang, M. Schwaab, J. Christopher, and J. Crabtree, “Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods”, Computational Mechanics, 43 (2008) 39–49, 10.1007/s00466-008-0261-7
@ARTICLE{Tezduyar08a, AUTHOR = {T. E.~Tezduyar and S.~Sathe and J.~Pausewang and M.~Schwaab and J.~Christopher and J.~Crabtree}, PAGES = {39--49}, JOURNAL = {Computational Mechanics}, VOLUME = {43}, TITLE = {Interface projection techniques for fluid--structure interaction modeling with moving-mesh methods}, YEAR = {2008}, DOI = {10.1007/s00466-008-0261-7} } Abstract:
The stabilized space-time fluid-structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) was applied to a number of 3D examples, including arterial fluid mechanics and parachute aerodynamics. Here we focus on the interface projection techniques that were developed as supplementary methods targeting the computational challenges associated with the geometric complexities of the fluid-structure interface. Although these supplementary techniques were developed in conjunction with the SSTFSI method and in the context of air-fabric interactions, they can also be used in conjunction with other moving-mesh methods, such as the Arbitrary Lagrangian-Eulerian (ALE) method, and in the context of other classes of FSI applications. The supplementary techniques currently consist of using split nodal values for pressure at the edges of the fabric and incompatible meshes at the air-fabric interfaces, the FSI Geometric Smoothing Technique (FSI-GST), and the Homogenized Modeling of Geometric Porosity (HMGP). Using split nodal values for pressure at the edges and incompatible meshes at the interfaces stabilizes the structural response at the edges of the membrane used in modeling the fabric. With the FSI-GST, the fluid mechanics mesh is sheltered from the consequences of the geometric complexity of the structure. With the HMGP, we bypass the intractable complexities of the geometric porosity by approximating it with an "equivalent", locally-varying fabric porosity. As test cases demonstrating how the interface projection techniques work, we compute the air-fabric interactions of windsocks, sails and ringsail parachutes. © 2008 Springer-Verlag.

[133]

T.E. Tezduyar, S. Ramakrishnan, and S. Sathe, “Stabilized formulations for incompressible flows with thermal coupling”, International Journal for Numerical Methods in Fluids, 57 (2008) 1189–1209, 10.1002/fld.1743
@ARTICLE{Tezduyar07j, AUTHOR = {T. E.~Tezduyar and S.~Ramakrishnan and S.~Sathe}, PAGES = {1189--1209}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {57}, TITLE = {Stabilized Formulations for Incompressible Flows with Thermal Coupling}, YEAR = {2008}, DOI = {10.1002/fld.1743} } Abstract:
We present applications of the stabilized finite element formulations developed for incompressible flows with thermal coupling to 2D and 3D test problems. The stabilized formulations are based on the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/ Petrov-Galerkin stabilizations and are supplemented with discontinuity capturing (DC), including the discontinuity-capturing directional dissipation. The stabilization and DC parameters associated with these formulations are also presented. The coupled fluid mechanics and temperature equations are solved with a direct coupling technique. The test problems computed include 2D and 3D natural convection, as well as a simplified 3D model of air circulation in a small data center. Copyright © 2008 John Wiley & Sons, Ltd.

[132]

T.E. Tezduyar, S. Sathe, M. Schwaab, and B.S. Conklin, “Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique”, International Journal for Numerical Methods in Fluids, 57 (2008) 601–629, 10.1002/fld.1633
@ARTICLE{Tezduyar07f, AUTHOR = {T. E.~Tezduyar and S.~Sathe and M.~Schwaab and B. S.~Conklin}, PAGES = {601--629}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {57}, TITLE = {Arterial Fluid Mechanics Modeling with the Stabilized Space--Time Fluid--Structure Interaction Technique}, YEAR = {2008}, DOI = {10.1002/fld.1633} } Abstract:
We present an overview of how the arterial fluid mechanics problems can be modeled with the stabilized space-time fluid-structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (TAFSM). The SSTFSI technique includes the enhancements introduced recently by the TAFSM to increase the scope, accuracy, robustness and efficiency of this class of techniques. The SSTFSI technique is supplemented with a number of special techniques developed for arterial fluid mechanics modeling. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, and the sequentially coupled arterial FSI (SCAFSI) technique. The recipe for pre-FSI computations is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is also based on that assumption. The need for an estimated zero-pressure arterial geometry is based on recognizing that the patient-specific image-based geometries correspond to time-averaged blood pressure values. In our arterial fluid mechanics modeling the arterial walls can be represented with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element is made of hyperelastic (Fung) material. Test computations are presented for cerebral and abdominal aortic aneurysms, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data. Copyright © 2007 John Wiley & Sons, Ltd.

[131]

M.A. Cruchaga, D.J. Celentano, and T.E. Tezduyar, “A numerical model based on the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) for flows with fluid–solid and fluid–fluid interfaces”, International Journal for Numerical Methods in Fluids, 54 (2007) 1021–1030, 10.1002/fld.1498
@ARTICLE{Cruchaga07a, AUTHOR = {M. A.~Cruchaga and D. J.~Celentano and T. E.~Tezduyar}, PAGES = {1021--1030}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {A Numerical Model Based on the {M}ixed {I}nterface-{T}racking/{I}nterface-{C}apturing {T}echnique ({MITICT}) for Flows with Fluid--Solid and Fluid--Fluid Interfaces}, YEAR = {2007}, DOI = {10.1002/fld.1498} } Abstract:
We propose a numerical model for computation of flow problems that involve both fluid-solid and fluid-fluid interfaces. The model is based on the mixed interface-tracking/interface-capturing technique (MITICT), which was introduced earlier for problems that involve both fluid-solid interfaces that are accurately tracked with a moving mesh method and fluid-fluid interfaces that are too complex to track and therefore treated with an interface-capturing technique. In our numerical model, fluid-solid interfaces are handled with the moving Lagrangian interface technique (MLIT) and fluid-fluid interfaces with the edge-tracked interface locator technique (ETILT). The mixed technique is tested in computation of a fluid-particle interaction problem in the presence of a fluid-fluid interface impacted by the particle. Copyright © 2007 John Wiley & Sons, Ltd.

[130]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm — Dependence of the effect on the aneurysm shape”, International Journal for Numerical Methods in Fluids, 54 (2007) 995–1009, 10.1002/fld.1497
@ARTICLE{Torii07a, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {995--1009}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {Numerical Investigation of the Effect of Hypertensive Blood Pressure on Cerebral Aneurysm --- {D}ependence of the Effect on the Aneurysm Shape}, YEAR = {2007}, DOI = {10.1002/fld.1497} } Abstract:
Fluid-structure interaction (FSI) computations of two cerebral aneurysms are carried out under hypertensive and normotensive blood pressures. Hypertensive blood pressure is one of the major risk factors in subarachnoid hemorrhage, which is mostly caused by the rupture of cerebral aneurysm. Since hemodynamic wall shear stress (WSS) is known to play an important role in aneurysm progression, investigating the WSS distribution in conjunction with hypertensive blood pressure is expected to provide a better understanding of aneurysms. The WSS distributions obtained from the simulations show that hypertensive blood pressure considerably affects one of the subjects but not the other. The effect is a wider spreading of the high WSS region on the aneurysm wall, which prevents the wall from weakening. It is also shown that the deformation of the aneurysm wall can alter the flow patterns in the aneurysm to diminish the stagnant flow near the apex, which is linked to the weakening of the wall. The effect of hypertensive blood pressure and wall deformation is shown to be highly dependent on individual aneurysm geometry, and that stresses the importance of subject-specific simulations. Copyright © 2007 John Wiley & Sons, Ltd.

[129]

Y. Bazilevs, V.M. Calo, T.E. Tezduyar, and T.J.R. Hughes, “YZβ discontinuity-capturing for advection-dominated processes with application to arterial drug delivery”, International Journal for Numerical Methods in Fluids, 54 (2007) 593–608, 10.1002/fld.1484
@ARTICLE{Bazilevs07a, AUTHOR = {Y.~Bazilevs and V. M.~Calo and T. E.~Tezduyar and T. J. R.~Hughes}, PAGES = {593--608}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {{YZ}$\beta$ Discontinuity-Capturing for Advection-Dominated Processes with Application to Arterial Drug Delivery}, YEAR = {2007}, DOI = {10.1002/fld.1484} } Abstract:
The YZβ discontinuity-capturing operator, recently introduced in (Encyclopedia of Computational Mechanics, Vol. 3, Fluids. Wiley: New York, 2004) in the context of compressible flows, is applied to a time-dependent, scalar advection-diffusion equation with the purpose of modelling drug delivery processes in blood vessels. The formulation is recast in a residual-based form, which reduces to the previously proposed formulation in the limit of zero diffusion and source term. The NURBS-based isogeometric analysis method, proposed by Hughes et al. (Comput. Methods Appl. Mech. Eng. 2005; 194:4135-4195), was used for the numerical tests. Effects of various parameters in the definition of the YZβ operator are examined on a model problem and the better performer is singled out. While for low-order B-spline functions discontinuity capturing is necessary to improve solution quality, we find that high-order, high-continuity B-spline discretizations produce sharp, nearly monotone layers without the aid of discontinuity capturing. Finally, we successfully apply the YZβ approach to the simulation of drug delivery in patient-specific coronary arteries. Copyright © 2007 John Wiley & Sons, Ltd.

[128]

K. Takizawa, K. Tanizawa, T. Yabe, and T.E. Tezduyar, “Ship hydrodynamics computations with the CIP method based on adaptive Soroban grids”, International Journal for Numerical Methods in Fluids, 54 (2007) 1011–1019, 10.1002/fld.1466
@ARTICLE{Takizawa07a, AUTHOR = {K.~Takizawa and K.~Tanizawa and T.~Yabe and T. E.~Tezduyar}, PAGES = {1011--1019}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {Ship Hydrodynamics Computations with the {CIP} Method Based on Adaptive {S}oroban Grids}, YEAR = {2007}, DOI = {10.1002/fld.1466} } Abstract:
The constrained interpolation profile/cubic interpolated pseudo-particle (CIP) combined unified procedure (CCUP) method (J. Phys. Soc. Jpn. 1991; 60:2105-2108), which is based on the CIP method (J. Comput. Phys. 1985; 61:261-268; J. Comput. Phys. 1987; 70:355-372; Comput. Phys. Commun. 1991; 66:219-232; J. Comput. Phys. 2001; 169:556-593) and the adaptive Soroban grid technique (J. Comput. Phys. 2004; 194:55-77) were combined in (Comput. Mech. 2006; published online) for computation of 3D fluid-object and fluid-structure interactions in the presence of free surfaces and fluid-fluid interfaces. Although the grid system is unstructured, it still has a very simple data structure and this facilitates computational efficiency. Despite the unstructured and collocated features of the grid, the method maintains high-order accuracy and computational robustness. Furthermore, the meshless feature of the combined technique brings freedom from mesh moving and distortion issues. In this paper, the combined technique is extended to ship hydrodynamics computations. We introduce a new way of computing the advective terms to increase the efficiency in that part of the computations. This is essential in ship hydrodynamics computations where the level of grid refinement needed near the ship surface and at the free surface results in very large grid sizes. The test cases presented are a test computation with a wave-making wedge and simulation of the hydrodynamics of a container ship. Copyright © 2007 John Wiley & Sons, Ltd.

[127]

T. Yabe, K. Takizawa, T.E. Tezduyar, and H.-N. Im, “Computation of fluid–solid and fluid–fluid interfaces with the CIP method based on adaptive Soroban grids — An overview”, International Journal for Numerical Methods in Fluids, 54 (2007) 841–853, 10.1002/fld.1473
@ARTICLE{Yabe07a, AUTHOR = {T.~Yabe and K.~Takizawa and T. E.~Tezduyar and Hyo-Nam Im}, PAGES = {841--853}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {Computation of Fluid--Solid and Fluid--Fluid Interfaces with the {CIP} Method Based on Adaptive {S}oroban Grids --- {A}n Overview}, YEAR = {2007}, DOI = {10.1002/fld.1473} } Abstract:
We provide an overview of how fluid-solid and fluid-fluid interfaces can be computed successfully with the constrained interpolation profile/ cubic interpolated pseudo-particle (CIP) method (J. Comput. Phys. 1985; 61:261-268; Comput. Phys. Commun. 1991; 66:219-232; Comput. Phys. Commun. 1991; 66: 233-242; J. Comput. Phys. 2001; 169:556-593) based on adaptive Soroban grids (J. Comput. Phys. 2004; 194:57-77). In this approach, the CIP combined unified procedure (CCUP) technique (J. Phys. Soc. Jpn 1991; 60:2105-2108), which is based on the CIP method, is combined with the adaptive Soroban grid technique. One of the superior features of the approach is that even though the grid system is unstructured, it still has a simple data structure that renders remarkable computational efficiency. Another superior feature is that despite the unstructured and collocated nature of the grid, high-order accuracy and computational robustness are maintained. In addition, because the Soroban grid technique does not have any elements or cells connecting the grid points, the approach does not involve mesh distortion limitations. While the details of the approach and several numerical examples were reported in (Comput. Mech. 2006; published online), our objective in this paper is to provide an easy-to-follow description of the key aspects of the approach. Copyright © 2007 John Wiley & Sons, Ltd.

[126]

T.E. Tezduyar, S. Sathe, T. Cragin, B. Nanna, B.S. Conklin, J. Pausewang, and M. Schwaab, “Modeling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics”, International Journal for Numerical Methods in Fluids, 54 (2007) 901–922, 10.1002/fld.1443
@ARTICLE{Tezduyar06c, AUTHOR = {T. E.~Tezduyar and S.~Sathe and T.~Cragin and B.~Nanna and B. S.~Conklin and J.~Pausewang and M.~Schwaab}, PAGES = {901--922}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {Modeling of Fluid--Structure Interactions with the Space--Time Finite Elements: {A}rterial Fluid Mechanics}, YEAR = {2007}, DOI = {10.1002/fld.1443} } Abstract:
The stabilized space-time fluid-structure interaction (SSTFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) are applied to FSI modelling in arterial fluid mechanics. Modelling of flow in arteries with aneurysm is emphasized. The SSTFSI techniques used are based on the deforming-spatial-domain/ stabilized space-time (DSD/SST) formulation and include the enhancements introduced recently by the T*AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The arterial structures can be modelled with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element can be made of linearly elastic or hyperelastic material. Test computations are presented for cerebral and abdominal aortic aneurysms and carotid-artery bifurcation, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data. Copyright © 2007 John Wiley & Sons, Ltd.

[125]

T.E. Tezduyar and S. Sathe, “Modeling of fluid–structure interactions with the space–time finite elements: Solution techniques”, International Journal for Numerical Methods in Fluids, 54 (2007) 855–900, 10.1002/fld.1430
@ARTICLE{Tezduyar06b, AUTHOR = {T. E.~Tezduyar and S.~Sathe}, PAGES = {855--900}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {Modeling of Fluid--Structure Interactions with the Space--Time Finite Elements: {S}olution Techniques}, YEAR = {2007}, DOI = {10.1002/fld.1430} } Abstract:
The space-time fluid-structure interaction (FSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) have been applied to a wide range of 3D computation of FSI problems, some as early as in 1994 and many with challenging complexities. In this paper, we review these space-time FSI techniques and describe the enhancements introduced recently by the T*AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The aspects of the FSI solution process enhanced include the deforming-spatial-domain/ stabilized space-time (DSD/SST) formulation, the fluid-structure interface conditions, the preconditioning techniques used in iterative solution of the linear equation systems, and a contact algorithm protecting the quality of the fluid mechanics mesh between the structural surfaces coming into contact. We present a number of 3D numerical examples computed with these new stabilized space-time FSI (SSTFSI) techniques. Copyright © 2007 John Wiley & Sons, Ltd.

[124]

F. Rispoli, R. Saavedra, A. Corsini, and T.E. Tezduyar, “Computation of inviscid compressible flows with the V-SGS stabilization and YZβ shock-capturing”, International Journal for Numerical Methods in Fluids, 54 (2007) 695–706, 10.1002/fld.1447
@ARTICLE{Rispoli07a, AUTHOR = {F.~Rispoli and R.~Saavedra and A.~Corsini and T. E.~Tezduyar}, PAGES = {695--706}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {54}, TITLE = {Computation of Inviscid Compressible Flows with the {V-SGS} Stabilization and {YZ}$\beta$ Shock-Capturing}, YEAR = {2007}, DOI = {10.1002/fld.1447} } Abstract:
The YZβ shock-capturing technique was introduced recently for use in combination with the streamline-upwind/Petrov-Galerkin formulation of compressible flows in conservation variables. The YZβ shock-capturing parameter is much simpler than an earlier parameter derived from the entropy variables for use in conservation variables. In this paper, we propose to use the YZβ shock-capturing in combination with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. We evaluate the performance of the V-SGS and YZβ combination in a number of standard, 2D test problems. Compared to the earlier shock-capturing parameter derived from the entropy variables, in addition to being much simpler, the YZβ shock-capturing parameter yields better shock quality in these test problems. Copyright © 2007 John Wiley & Sons, Ltd.

[123]

K. Takizawa, T. Yabe, Y. Tsugawa, T.E. Tezduyar, and H. Mizoe, “Computation of free–surface flows and fluid–object interactions with the CIP method based on adaptive meshless Soroban grids”, Computational Mechanics, 40 (2007) 167–183, 10.1007/s00466-006-0093-2
@ARTICLE{Takizawa06a, AUTHOR = {K.~Takizawa and T.~Yabe and Y.~Tsugawa and T. E.~Tezduyar and H.~Mizoe}, PAGES = {167--183}, JOURNAL = {Computational Mechanics}, VOLUME = {40}, TITLE = {Computation of Free--Surface Flows and Fluid--Object Interactions with the {CIP} Method Based on Adaptive Meshless {S}oroban Grids}, YEAR = {2007}, DOI = {10.1007/s00466-006-0093-2} } Abstract:
The CIP Method [J comput phys 61:261-268 1985; J comput phys 70:355-372, 1987; Comput phys commun 66:219-232 1991; J comput phys 169:556-593, 2001] and adaptive Soroban grid [J comput phys 194:57-77, 2004] are combined for computation of three- dimensional fluid-object and fluid-structure interactions, while maintaining high-order accuracy. For the robust computation of free-surface and multi-fluid flows, we adopt the CCUP method [Phys Soc Japan J 60:2105-2108 1991]. In most of the earlier computations, the CCUP method was used with a staggered-grid approach. Here, because of the meshless nature of the Soroban grid, we use the CCUP method with a collocated-grid approach. We propose an algorithm that is stable, robust and accurate even with such collocated grids. By adopting the CIP interpolation, the accuracy is largely enhanced compared to linear interpolation. Although this grid system is unstructured, it still has a very simple data structure. © Springer Verlag 2007.

[122]

T.E. Tezduyar and S. Sathe, “Enhanced-discretization selective stabilization procedure (EDSSP)”, Computational Mechanics, 38 (2006) 456–468, 10.1007/s00466-006-0056-7
@ARTICLE{Tezduyar05g, AUTHOR = {T. E.~Tezduyar and S.~Sathe}, PAGES = {456--468}, JOURNAL = {Computational Mechanics}, VOLUME = {38}, TITLE = {Enhanced-Discretization Selective Stabilization Procedure ({EDSSP})}, YEAR = {2006}, DOI = {10.1007/s00466-006-0056-7} } Abstract:
The enhanced-discretization selective stabilization procedure (EDSSP) provides a multiscale framework for applying numerical stabilization selectively at different scales. The EDSSP is based on the enhanced-discretization, multiscale function space concept underlying the enhanced- discretization successive update method (EDSUM). The EDSUM is a multi-level iteration method designed for computation of the flow behavior at small scales. It has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. This is accomplished without assuming that the small-scale trial or test functions vanish at the borders between the neighboring large-scale elements of the enhanced-discretization zones. This facilitates unrestricted movement of small-scale flow patterns from one large-scale element to another without any constraints at the border between the two elements. The enhanced-discretization concept underlying the EDSUM can also facilitate using different stabilizations for equations or unknowns corresponding to different scales. In this paper we propose a version of the EDSSP where the SUPG and PSPG stabilizations are used for unknowns corresponding to both the large and small scales but the discontinuity-capturing stabilizations are used for unknowns corresponding to only the small scales. We also propose a version where a linear discontinuity-capturing is used for the small-scale unknowns and a nonlinear discontinuity-capturing is used for the large-scale unknowns. We evaluate the performances of these versions of the EDSSP with test problems governed by the advection-diffusion equations.

[121]

A. Corsini, F. Rispoli, A. Santoriello, and T.E. Tezduyar, “Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation”, Computational Mechanics, 38 (2006) 356–364, 10.1007/s00466-006-0045-x
@ARTICLE{Corsini06a, AUTHOR = {A.~Corsini and F.~Rispoli and A.~Santoriello and T. E.~Tezduyar}, PAGES = {356--364}, JOURNAL = {Computational Mechanics}, VOLUME = {38}, TITLE = {Improved Discontinuity-Capturing Finite Element Techniques for Reaction Effects in Turbulence Computation}, YEAR = {2006}, DOI = {10.1007/s00466-006-0045-x} } Abstract:
Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ε, k-ε -v 2-f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199-255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217-284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307-325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387-401, 1995) has been introduced, and this approach, in principle, can deal with advection-diffusion- reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925-2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797-4823, 2005). Model problems and industrial test cases are computed to show the potential of the proposed methods in simulation of turbulent flows.

[120]

M.A. Cruchaga, D.J. Celentano, and T.E. Tezduyar, “Collapse of a liquid column: numerical simulation and experimental validation”, Computational Mechanics, 39 (2007) 453–476, 10.1007/s00466-006-0043-z
@ARTICLE{Cruchaga06a, AUTHOR = {M. A.~Cruchaga and D. J.~Celentano and T. E.~Tezduyar}, PAGES = {453--476}, JOURNAL = {Computational Mechanics}, VOLUME = {39}, TITLE = {Collapse of a Liquid Column: Numerical Simulation and Experimental Validation}, YEAR = {2007}, DOI = {10.1007/s00466-006-0043-z} } Abstract:
This paper is focused on the numerical and experimental analyses of the collapse of a liquid column. The measurements of the interface position in a set of experiments carried out with shampoo and water for two different initial column aspect ratios are presented together with the corresponding numerical predictions. The experimental procedure was found to provide acceptable recurrence in the observation of the interface evolution. Basic models describing some of the relevant physical aspects, e.g. wall friction and turbulence, are included in the simulations. Numerical experiments are conducted to evaluate the influence of the parameters involved in the modeling by comparing the results with the data from the measurements. The numerical predictions reasonably describe the physical trends. © Springer Verlag 2007.

[119]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures”, Computational Mechanics, 38 (2006) 482–490, 10.1007/s00466-006-0065-6
@ARTICLE{Torii06a, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {482--490}, JOURNAL = {Computational Mechanics}, VOLUME = {38}, TITLE = {Fluid--Structure Interaction Modeling of Aneurysmal Conditions with High and Normal Blood Pressures}, YEAR = {2006}, DOI = {10.1007/s00466-006-0065-6} } Abstract:
Hemodynamic factors like the wall shear stress play an important role in cardiovascular diseases. To investigate the influence of hemodynamic factors in blood vessels, the authors have developed a numerical fluid-structure interaction (FSI) analysis technique. The objective is to use numerical simulation as an effective tool to predict phenomena in a living human body. We applied the technique to a patient-specific arterial model, and with that we showed the effect of wall deformation on the WSS distribution. In this paper, we compute the interaction between the blood flow and the arterial wall for a patient-specific cerebral aneurysm with various hemodynamic conditions, such as hypertension. We particularly focus on the effects of hypertensive blood pressure on the interaction and the WSS, because hypertension is reported to be a risk factor in rupture of aneurysms. We also aim to show the possibility of FSI computations with hemodynamic conditions representing those risk factors in cardiovascular disease. The simulations show that the transient behavior of the interaction under hypertensive blood pressure is significantly different from the interaction under normal blood pressure. The transient behavior of the blood-flow velocity, and the resulting WSS and the mechanical stress in the aneurysmal wall, are significantly affected by hypertension. The results imply that hypertension affects the growth of an aneurysm and the damage in arterial tissues.

[118]

T.E. Tezduyar, M. Senga, and D. Vicker, “Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing”, Computational Mechanics, 38 (2006) 469–481, 10.1007/s00466-005-0025-6
@ARTICLE{Tezduyar05f, AUTHOR = {T. E.~Tezduyar and M.~Senga and D.~Vicker}, PAGES = {469--481}, JOURNAL = {Computational Mechanics}, VOLUME = {38}, TITLE = {Computation of Inviscid Supersonic Flows around Cylinders and Spheres with the {SUPG} Formulation and {YZ}$\beta$ Shock-Capturing}, YEAR = {2006}, DOI = {10.1007/s00466-005-0025-6} } Abstract:
Numerical experiments with inviscid supersonic flows around cylinders and spheres are carried out to evaluate the stabilization and shock-capturing parameters introduced recently for the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation of compressible flows based on conservation variables. The tests with the cylinders are carried out for both structured and unstructured meshes. The new shock-capturing parameters, which we call "YZβ Shock-Capturing", are compared to earlier SUPG parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for unstructured meshes with triangular and tetrahedral elements. Furthermore, the results obtained with YZβ Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code.

[117]

L. Catabriga, A.L.G.A. Coutinho, and T.E. Tezduyar, “Compressible flow SUPG stabilization parameters computed from degree-of-freedom submatrices”, Computational Mechanics, 38 (2006) 334–343, 10.1007/s00466-006-0033-1
@ARTICLE{Catabriga05b, AUTHOR = {L.~Catabriga and A. L. G. A.~Coutinho and T. E.~Tezduyar}, PAGES = {334--343}, JOURNAL = {Computational Mechanics}, VOLUME = {38}, TITLE = {Compressible Flow {SUPG} Stabilization Parameters Computed from Degree-of-Freedom Submatrices}, YEAR = {2006}, DOI = {10.1007/s00466-006-0033-1} } Abstract:
We present, for the SUPG formulation of inviscid compressible flows, stabilization parameters defined based on the degree-of-freedom submatrices of the element-level matrices. With 2D steady-state test problems involving supersonic flows and shocks, we compare these stabilization parameters with the ones defined based on the full element-level matrices. We also compare them to the stabilization parameters introduced in the earlier development stages of the SUPG formulation of compressible flows. In all cases the formulation includes a shock-capturing term involving a shock-capturing parameter. We investigate the difference between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every nonlinear iteration within a time step. The formulation includes, as an option, an algorithmic feature that is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected.

[116]

T.E. Tezduyar, S. Sathe, and K. Stein, “Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 5743–5753, 10.1016/j.cma.2005.08.023
@ARTICLE{Tezduyar05a, AUTHOR = {T. E.~Tezduyar and S.~Sathe and K.~Stein}, PAGES = {5743--5753}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {195}, TITLE = {Solution Techniques for the Fully-Discretized Equations in Computation of Fluid--Structure Interactions with the Space--Time Formulations}, YEAR = {2006}, DOI = {10.1016/j.cma.2005.08.023} } Abstract:
We provide an overview of the solution techniques we have developed for the fully discretized equations encountered at every time step in computation of fluid-structure interactions with the space-time techniques. These coupled, nonlinear equations are generated from the finite element discretization of the governing equations for the fluid mechanics, structural mechanics and the motion of the fluid mechanics mesh. The fluid mechanics equations are discretized with the deforming-spatial-domain/stabilized space-time formulation. The mesh motion is governed by the equations of elasticity, with the smaller elements stiffened in the finite element formulation. The coupled, fully discretized equations are solved with the block-iterative, quasi-direct and direct coupling methods. We present numerical examples with incompressible flows and membrane and cable structures. © 2005 Elsevier B.V. All rights reserved.

[115]

J.E. Akin, T.E. Tezduyar, and M. Ungor, “Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT)”, Computers & Fluids, 36 (2007) 2–11, 10.1016/j.compfluid.2005.07.008
@ARTICLE{Akin05a, AUTHOR = {J. E.~Akin and T. E.~Tezduyar and M.~Ungor}, PAGES = {2--11}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {Computation of Flow Problems with the Mixed Interface-Tracking/Interface-Capturing Technique {(MITICT)}}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.07.008} } Abstract:
In computation of flow problems with fluid-solid interfaces, an interface-tracking technique, where the fluid mesh moves to track the interface, would allow us to have full control of the resolution of the fluid mesh in the boundary layers. With an interface-capturing technique (or an interface locator technique in the more general case), on the other hand, independent of how accurately the interface geometry is represented, the resolution of the fluid mesh in the boundary layer will be limited by the resolution of the fluid mesh at the interface. In computation of flow problems with fluid-fluid interfaces where the interface is too complex or unsteady to track while keeping the remeshing frequency under control, interface-capturing techniques, with enhanced-discretization as needed, could be used as more flexible alternatives. Sometimes we may need to solve flow problems with both fluid-solid interfaces and complex or unsteady fluid-fluid interfaces. The Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) was introduced for computation of flow problems that involve both interfaces that can be accurately tracked with a moving mesh method and interfaces that are too complex or unsteady to be tracked and therefore require an interface-capturing technique. As the interface-tracking technique, we use the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation. The interface-capturing technique rides on this, and is based on solving over a moving mesh, in addition to the Navier-Stokes equations, the advection equation governing the time-evolution of the interface function. For the computations reported in this paper, as interface-capturing technique we are using one of the versions of the Edge-Tracked Interface Locator Technique (ETILT). © 2005 Elsevier Ltd. All rights reserved.

[114]

F. Rispoli, A. Corsini, and T.E. Tezduyar, “Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD)”, Computers & Fluids, 36 (2007) 121–126, 10.1016/j.compfluid.2005.07.004
@ARTICLE{Rispoli05a, AUTHOR = {F.~Rispoli and A.~Corsini and T. E.~Tezduyar}, PAGES = {121--126}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {Finite Element Computation of Turbulent Flows with the Discontinuity-Capturing Directional Dissipation {(DCDD)}}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.07.004} } Abstract:
The streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods are among the most popular stabilized formulations in finite element computation of flow problems. The discontinuity-capturing directional dissipation (DCDD) was first introduced as a complement to the SUPG and PSPG stabilizations for the computation of incompressible flows in the presence of sharp solution gradients. The DCDD stabilization takes effect where there is a sharp gradient in the velocity field and introduces dissipation in the direction of that gradient. The length scale used in defining the DCDD stabilization is based on the solution gradient. Here we describe how the DCDD stabilization, in combination with the SUPG and PSPG stabilizations, can be applied to computation of turbulent flows. We examine the similarity between the DCDD stabilization and a purely dissipative energy cascade model. To evaluate the performance of the DCDD stabilization, we compute as test problem a plane channel flow at friction Reynolds number Reτ = 180. © 2005 Elsevier Ltd. All rights reserved.

[113]

T. Washio, T. Hisada, H. Watanabe, and T.E. Tezduyar, “A robust preconditioner for fluid–structure interaction problems”, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 4027–4047, 10.1016/j.cma.2004.10.001
@ARTICLE{Washio05a, AUTHOR = {T.~Washio and T.~Hisada and H.~Watanabe and T. E.~Tezduyar}, PAGES = {4027--4047}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {194}, TITLE = {A robust preconditioner for fluid--structure interaction problems}, YEAR = {2005}, DOI = {10.1016/j.cma.2004.10.001} } Abstract:
Two preconditioners are presented for equation systems of strongly coupled fluid-structure interaction computations where the structure is modeled by shell elements. These preconditioners fall into the general category of incomplete LU factorization. The two differ mainly in whether the coefficient matrix is factorized node by node or variable-by-variable. In the variable-wise preconditioner, a modified Schur complement system for pressure is solved approximately with a few iterations using a special preconditioner. The efficiencies of the two preconditioners are compared for different finite element formulations of the fluid mechanics part, including formulations with SUPG and PSPG stabilizations. © 2004 Elsevier B.V. All rights reserved.

[112]

T.E. Tezduyar and M. Senga, “SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing”, Computers & Fluids, 36 (2007) 147–159, 10.1016/j.compfluid.2005.07.009
@ARTICLE{Tezduyar05d, AUTHOR = {T. E.~Tezduyar and M.~Senga}, PAGES = {147--159}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {{SUPG} Finite Element Computation of Inviscid Supersonic Flows with {YZ}$\beta$ Shock-Capturing}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.07.009} } Abstract:
Stabilization and shock-capturing parameters introduced recently for the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation of compressible flows based on conservation variables are assessed in test computations with inviscid supersonic flows and different types of finite element meshes. The new shock-capturing parameters, categorized as "YZβ Shock-Capturing" in this paper, are compared to earlier parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for triangular elements. © 2005 Elsevier Ltd. All rights reserved.

[111]

S. Sathe, R. Benney, R. Charles, E. Doucette, J. Miletti, M. Senga, K. Stein, and T.E. Tezduyar, “Fluid–structure interaction modeling of complex parachute designs with the space–time finite element techniques”, Computers & Fluids, 36 (2007) 127–135, 10.1016/j.compfluid.2005.07.010
@ARTICLE{Sathe05a, AUTHOR = {S.~Sathe and R.~Benney and R.~Charles and E.~Doucette and J.~Miletti and M.~Senga and K.~Stein and T. E.~Tezduyar}, PAGES = {127--135}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {Fluid--Structure Interaction Modeling of Complex Parachute Designs with the Space--Time Finite Element Techniques}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.07.010} } Abstract:
In recent years we introduced a number of enhancements to the space-time techniques we developed for computer modeling of Fluid-Structure Interaction (FSI) problems. These enhancements, which include more sophisticated fluid-structure coupling and improved mesh generation, are enabling us to address more of the computational challenges involved. Our objective here is to demonstrate the robustness of these techniques in FSI modeling of parachutes involving complex designs. As a numerical example, we have selected a conceptual parachute design with geometric complexities resembling those seen in some of the advanced parachute designs proposed and tested in recent times. We describe our FSI modeling techniques and how we compute the descent and glide performance of this conceptual parachute design. © 2005 Elsevier Ltd. All rights reserved.

[110]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Influence of wall elasticity in patient-specific hemodynamic simulations”, Computers & Fluids, 36 (2007) 160–168, 10.1016/j.compfluid.2005.07.014
@ARTICLE{Torii05a, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {160--168}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {Influence of Wall Elasticity in Patient-Specific Hemodynamic Simulations}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.07.014} } Abstract:
Recent reports indicate that the rupture risk for cerebral aneurysms is less than the risk of surgical complications. Being able to predict the rupture of aneurysms would help making better-informed decisions and avoiding unnecessary surgical operations. The wall shear stress is known to play an important role in vascular diseases. We carry out computational fluid-structure interaction analyses to investigate the influence of the arterial-wall deformation on the hemodynamic factors, including the wall shear stress distribution. The results show various patterns of this influence, depending very much on the arterial geometry. © 2005 Elsevier Ltd. All rights reserved.

[109]

L. Catabriga, A.L.G.A. Coutinho, and T.E. Tezduyar, “Compressible flow SUPG parameters computed from element matrices”, Communications in Numerical Methods in Engineering, 21 (2005) 465–476, 10.1002/cnm.759
@ARTICLE{Catabriga05a, AUTHOR = {L.~Catabriga and A. L. G. A.~Coutinho and T. E.~Tezduyar}, PAGES = {465--476}, JOURNAL = {Communications in Numerical Methods in Engineering}, VOLUME = {21}, TITLE = {Compressible Flow {SUPG} Parameters Computed from Element Matrices}, YEAR = {2005}, DOI = {10.1002/cnm.759} } Abstract:
We present, for the SUPG formulation of inviscid compressible flows with shocks, stabilization parameters defined based on the element-level matrices. These definitions are expressed in terms of the ratios of the norms of the matrices and take into account the flow field, the local length scales, and the time step size. Calculations of these stabilization parameters are straightforward and do not require explicit expressions for length or velocity scales. We compare the performance of these stabilization parameters, accompanied by a shock-capturing parameter introduced earlier, with the performance of a stabilization parameter introduced earlier, accompanied by the same shock-capturing parameter. We investigate the performance difference between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every non-linear iteration within a time step. We also investigate the influence of activating an algorithmic option that was introduced earlier, which is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected. Copyright © 2005 John Wiley & Sons, Ltd.

[108]

T.E. Tezduyar, “Finite elements in fluids: Special methods and enhanced solution techniques”, Computers & Fluids, 36 (2007) 207–223, 10.1016/j.compfluid.2005.02.010
@ARTICLE{Tezduyar04n, AUTHOR = {T. E.~Tezduyar}, PAGES = {207--223}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {Finite Elements in Fluids: {S}pecial Methods and Enhanced Solution Techniques}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.02.010} } Abstract:
As a sequel to "Finite elements in fluids: stabilized formulations and moving boundaries and interfaces" [Tezduyar TE. Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids, in press, doi:10.1016/j.compfluid.2005.02.011.], in this article we provide an overview of the special methods and enhanced solution techniques we developed in conjunction with the methods described in the accompanying paper. The methods and ideas highlighted here were introduced to increase the scope and accuracy of the stabilized formulations and interface-tracking and interface-capturing techniques highlighted in the accompanying paper. They include special methods for fluid-object interactions, for flows involving objects in fast, linear or rotational relative motion, and for two-fluid flows. They also include enhanced solutions techniques, where we have enhancement in spatial discretization, enhancement in time discretization, and enhancement in iterative solution of non-linear and linear equation systems. © 2005 Elsevier Ltd. All rights reserved.

[107]

T.E. Tezduyar, “Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces”, Computers & Fluids, 36 (2007) 191–206, 10.1016/j.compfluid.2005.02.011
@ARTICLE{Tezduyar04m, AUTHOR = {T. E.~Tezduyar}, PAGES = {191--206}, JOURNAL = {Computers \& Fluids}, VOLUME = {36}, TITLE = {Finite Elements in Fluids: {S}tabilized Formulations and Moving Boundaries and Interfaces}, YEAR = {2007}, DOI = {10.1016/j.compfluid.2005.02.011} } Abstract:
We provide an overview of the finite element methods we developed for fluid dynamics problems. We focus on stabilized formulations and moving boundaries and interfaces. The stabilized formulations are the streamline-upwind/Petrov-Galerkin (SUPG) formulations for compressible and incompressible flows and the pressure-stabilizing/Petrov-Galerkin (PSPG) formulation for incompressible flows. These are supplemented with the discontinuity-capturing directional dissipation (DCDD) for incompressible flows and the shock-capturing terms for compressible flows. Determination of the stabilization and shock-capturing parameters used in these formulations is highlighted. Moving boundaries and interfaces include free surfaces, two-fluid interfaces, fluid-object and fluid-structure interactions, and moving mechanical components. The methods developed for this class of problems can be classified into two main categories: interface-tracking and interface-capturing techniques. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, where the mesh moves to track the interface. The interface-capturing techniques were developed for two-fluid flows. They are based on the stabilized formulation, over typically non-moving meshes, of both the flow equations and an advection equation. The advection equation governs the time-evolution of an interface function marking the interface location. We also describe some of the additional methods and ideas we introduced to increase the scope and accuracy of these two classes of techniques. Among them is the enhanced-discretization interface-capturing technique (EDICT), which was developed to increase the accuracy in capturing the interface. Also among them is the mixed interface-tracking/interface-capturing technique (MITICT), which was introduced for problems that involve both interfaces that can be accurately tracked with a moving-mesh method and interfaces that call for an interface-capturing technique. © 2005 Elsevier Ltd. All rights reserved.

[106]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Computer modeling of cardiovascular fluid–structure interactions with the Deforming-Spatial-Domain/Stabilized Space–Time formulation”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 1885–1895, 10.1016/j.cma.2005.05.050
@ARTICLE{Torii04c, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {1885--1895}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {195}, TITLE = {Computer Modeling of Cardiovascular Fluid--Structure Interactions with the {D}eforming-{S}patial-{D}omain/{S}tabilized {S}pace--{T}ime Formulation}, YEAR = {2006}, DOI = {10.1016/j.cma.2005.05.050} } Abstract:
Hemodynamic factors such as the wall shear stress are believed to affect a number of cardiovascular diseases including atherosclerosis and aneurysm. Since resolving phenomena in a living human body is currently beyond the capabilities of in vivo measurement techniques, computer modeling is expected to play an important role in gaining a better understanding of the relationship between the cardiovascular diseases and the hemodynamic factors. We have developed a computer modeling technique for cardiovascular hemodynamic simulations. With this modeling technique, patient-specific 3D geometry of an artery can be analyzed. We take into account some of the important factors in human body for the purpose of demonstrating in vivo situations in a virtual world. The interaction between the blood flow and the deformation of the arterial walls is a factor that we are specifically focusing on. For such fluid-structure interactions, we have developed a computer modeling tool based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation. This simulation tool is applied to a patient-specific model under pulsatile blood flow conditions. The simulations show that the flow behavior with compliant arterial walls is different from what we see with rigid arterial walls. Consequently, the distribution of the wall shear stress on the compliant arterial walls is significantly different from that on the rigid arterial walls. We deduce that the compliance of the arterial walls needs to be taken into account in cardiovascular hemodynamic simulations, and the computer modeling tool we have developed can be effective in investigation of cardiovascular diseases. © 2005 Elsevier B.V. All rights reserved.

[105]

T.E. Tezduyar and A. Sameh, “Parallel finite element computations in fluid mechanics”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 1872–1884, 10.1016/j.cma.2005.05.038
@ARTICLE{Tezduyar04p, AUTHOR = {T. E.~Tezduyar and A.~Sameh}, PAGES = {1872--1884}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {195}, TITLE = {Parallel Finite Element Computations in Fluid Mechanics}, YEAR = {2006}, DOI = {10.1016/j.cma.2005.05.038} } Abstract:
We provide an overview of the role of parallel finite element computations in fluid mechanics. We emphasize the class of flow problems involving moving boundaries and interfaces. Some of the computationally most challenging flow problems, such as fluid-object and fluid-structure interactions as well as free-surface and two-fluid flows, belong to this class. In the development of the methods targeting this class of problems, the computational challenges involved need to be addressed in such a way that 3D computation of complex applications can be carried out efficiently on parallel computers. This requirement has to be one of the key factors in designing various components of the overall solution approach, such as solution techniques for the discretized equations and mesh update methods for handling the changes in the spatial domain occupied by the fluid. This overview includes a description of how the computational challenges are addressed and how the computational schemes can be enhanced with special preconditioning techniques. © 2005 Elsevier B.V. All rights reserved.

[104]

T.E. Tezduyar and M. Senga, “Stabilization and shock-capturing parameters in SUPG formulation of compressible flows”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 1621–1632, 10.1016/j.cma.2005.05.032
@ARTICLE{Tezduyar04o, AUTHOR = {T. E.~Tezduyar and M.~Senga}, PAGES = {1621--1632}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {195}, TITLE = {Stabilization and Shock-Capturing Parameters in {SUPG} Formulation of Compressible Flows}, YEAR = {2006}, DOI = {10.1016/j.cma.2005.05.032} } Abstract:
The streamline-upwind/Petrov-Galerkin (SUPG) formulation is one of the most widely used stabilized methods in finite element computation of compressible flows. It includes a stabilization parameter that is known as "τ". Typically the SUPG formulation is used in combination with a shock-capturing term that provides additional stability near the shock fronts. The definition of the shock-capturing term includes a shock-capturing parameter. In this paper, we describe, for the finite element formulation of compressible flows based on conservation variables, new ways for determining the τ and the shock-capturing parameter. The new definitions for the shock-capturing parameter are much simpler than the one based on the entropy variables, involve less operations in calculating the shock-capturing term, and yield better shock quality in the test computations. © 2005 Elsevier B.V. All rights reserved.

[103]

T.E. Tezduyar, “Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 2983–3000, 10.1016/j.cma.2004.09.018
@ARTICLE{Tezduyar04i, AUTHOR = {T. E.~Tezduyar}, PAGES = {2983--3000}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {195}, TITLE = {Interface-Tracking and Interface-Capturing Techniques for Finite Element Computation of Moving Boundaries and Interfaces}, YEAR = {2006}, DOI = {10.1016/j.cma.2004.09.018} } Abstract:
We provide an overview of some of the interface-tracking and interface-capturing techniques we developed for finite element computation of flow problems with moving boundaries and interfaces. This category of flow problems includes fluid-particle, fluid-object and fluid-structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. Both classes of techniques are based on stabilized formulations. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, where the mesh moves to track the interface. The interface-capturing techniques, developed primarily for free-surface and two-fluid interface flows, are formulated typically over non-moving meshes, using an advection equation in addition to the flow equations. The advection equation governs the evolution of an interface function that marks the location of the interface. We also highlight some of the methods we developed to increase the scope and accuracy of these two classes of techniques. © 2005 Elsevier B.V. All rights reserved.

[102]

M.A. Cruchaga, D.J. Celentano, and T.E. Tezduyar, “Moving-interface computations with the edge-tracked interface locator technique (ETILT)”, International Journal for Numerical Methods in Fluids, 47 (2005) 451–469, 10.1002/fld.825
@ARTICLE{Cruchaga04a, AUTHOR = {M. A.~Cruchaga and D. J.~Celentano and T. E.~Tezduyar}, PAGES = {451--469}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {47}, TITLE = {Moving-Interface Computations with the Edge-Tracked Interface Locator Technique {(ETILT)}}, YEAR = {2005}, DOI = {10.1002/fld.825} } Abstract:
We describe, for simulation of flows with moving interfaces, a computational method based on the edge-tracked interface locator technique (ETILT). The method described has been designed by bearing in mind the ease in managing a node-based interface representation and the interface sharpness and volume conservation features of the Moving Lagrangian Interface Technique. We evaluate the performance of the method with a number of test problems: Filling of a step cavity, gravity-driven flow of an aluminium alloy in an obstructed channel, collapse of a liquid column, and the bore problem. Copyright © 2004 John Wiley & Sons, Ltd.

[101]

T.E. Tezduyar and S. Sathe, “Enhanced-discretization successive update method (EDSUM)”, International Journal for Numerical Methods in Fluids, 47 (2005) 633–654, 10.1002/fld.836
@ARTICLE{Tezduyar04f, AUTHOR = {T. E.~Tezduyar and S.~Sathe}, PAGES = {633--654}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {47}, TITLE = {Enhanced-Discretization Successive Update Method {(EDSUM)}}, YEAR = {2005}, DOI = {10.1002/fld.836} } Abstract:
The enhanced-discretization successive update method (EDSUM) is a multi-level iteration method designed for computation of the flow behaviour at small scales. As an enhancement in iterative solution of non-linear and linear equation systems, the EDSUM is one of the enhanced discretization and solution techniques developed for more effective computation of complex flow problems. It complements techniques based on enhancement in spatial discretization and based on enhancement in time discretization in the context of a space-time formulation. It is closely related to the enhanced-discretization interface-capturing technique (EDICT), as the function spaces used in the EDSUM are very similar to those used in the EDICT. The EDSUM also has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. With a number of test computations for steady-state problems governed by the advection-diffusion equation, we demonstrate that the EDSUM has the potential to become a competitive technique for computation of flow behaviour at small scales. Copyright © 2004 John Wiley & Sons, Ltd.

[100]

T.E. Tezduyar, S. Sathe, R. Keedy, and K. Stein, “Space–time finite element techniques for computation of fluid–structure interactions”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 2002–2027, 10.1016/j.cma.2004.09.014
@ARTICLE{Tezduyar04e, AUTHOR = {T. E.~Tezduyar and S.~Sathe and R.~Keedy and K.~Stein}, PAGES = {2002--2027}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {195}, TITLE = {Space--Time Finite Element Techniques for Computation of Fluid--Structure Interactions}, YEAR = {2006}, DOI = {10.1016/j.cma.2004.09.014} } Abstract:
We describe the space-time finite element techniques we developed for computation of fluid-structure interaction (FSI) problems. Among these techniques are the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation and its special version, and the mesh update methods, including the solid-extension mesh moving technique (SEMMT). Also among these techniques are the block-iterative, quasi-direct and direct coupling methods for the solution of the fully discretized, coupled fluid and structural mechanics equations. We present some test computations for the mesh moving techniques described. We also present numerical examples where the fluid is governed by the Navier-Stokes equations of incompressible flows and the structure is governed by the membrane and cable equations. Overall, we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of FSI problems. © 2005 Elsevier B.V. All rights reserved.

[99]

K. Stein, T.E. Tezduyar, S. Sathe, R. Benney, and R. Charles, “Fluid-structure interaction modeling of parachute soft-landing dynamics”, International Journal for Numerical Methods in Fluids, 47 (2005) 619–631, 10.1002/fld.835
@ARTICLE{Stein04a, AUTHOR = {K.~Stein and T. E.~Tezduyar and S.~Sathe and R.~Benney and R.~Charles}, PAGES = {619--631}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {47}, TITLE = {Fluid-Structure Interaction Modeling of Parachute Soft-Landing Dynamics}, YEAR = {2005}, DOI = {10.1002/fld.835} } Abstract:
Soft landing of a payload with the aid of a retraction device is an important aspect in cargo parachute operations. Accurate simulation of this class of parachute operations with a computer model that takes into account the fluid-structure interactions involved would complement drop tests and support the design of cargo parachute systems. We describe the computational methods developed for this purpose, demonstrate how the computational model works in investigation of different soft-landing conditions, and show a good correlation between the data from our simulations and drop tests. Copyright © 2004 John Wiley & Sons, Ltd.

[98]

J.E. Akin and T.E. Tezduyar, “Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements”, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 1909–1922, 10.1016/j.cma.2003.12.050
@ARTICLE{Akin03a, AUTHOR = {J. E.~Akin and T. E.~Tezduyar}, PAGES = {1909--1922}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {193}, TITLE = {Calculation of the Advective Limit of the {SUPG} Stabilization Parameter for Linear and Higher-Order Elements}, YEAR = {2004}, DOI = {10.1016/j.cma.2003.12.050} } Abstract:
We investigate, for linear and higher-order elements, various ways of calculating the advective limit of the stabilization parameter ("τ") used in the streamline-upwind/Petrov-Galerkin (SUPG) formulation of flow problems. In the context of a pure advection test problem, we compare the "UGN-based", element-matrix-based, and element-node-based calculations of the advective limit of the τ. Our investigation shows that the performances of the "UGN-based" and element-matrix-based τ definitions are comparable, with the element-matrix-based definition yielding somewhat lower τ values. We also show that for both definitions, as the polynomial orders increase, the τ values decrease, as they should. © 2004 Elsevier B.V. All rights reserved.

[97]

T.E. Tezduyar and S. Sathe, “Enhanced-approximation linear solution technique (EALST)”, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 2033–2049, 10.1016/j.cma.2003.12.045
@ARTICLE{Tezduyar03c, AUTHOR = {T. E.~Tezduyar and S.~Sathe}, PAGES = {2033--2049}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {193}, TITLE = {Enhanced-Approximation Linear Solution Technique {(EALST)}}, YEAR = {2004}, DOI = {10.1016/j.cma.2003.12.045} } Abstract:
The enhanced discretization and solution techniques are among the advanced computational methods we rely on in simulation and modeling of complex flow problems, including those with moving boundaries and interfaces. The set of enhanced discretization and solution techniques includes those based on enhancement in spatial discretization, enhancement in time discretization, and enhancement in iterative solution of nonlinear and linear equation systems. The enhanced-approximation linear solution technique (EALST) was introduced to increase the performance of the iterative technique used in solution of the linear equation systems when some parts of the computational domain may offer more of a challenge for the iterative method than the others. The EALST can be used for computations based on semi-discrete or space-time formulations. © 2004 Elsevier B.V. All rights reserved.

[96]

K. Stein, T.E. Tezduyar, and R. Benney, “Automatic mesh update with the solid-extension mesh moving technique”, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 2019–2032, 10.1016/j.cma.2003.12.046
@ARTICLE{Stein03a, AUTHOR = {K.~Stein and T. E.~Tezduyar and R.~Benney}, PAGES = {2019--2032}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {193}, TITLE = {Automatic Mesh Update with the Solid-Extension Mesh Moving Technique}, YEAR = {2004}, DOI = {10.1016/j.cma.2003.12.046} } Abstract:
In computation of fluid-structure interactions involving large displacements, we use a mesh update method composed of mesh moving and remeshing-as-needed. For problems with complex geometries, we need automatic mesh moving techniques that reduce the need for remeshing. We also would like that these mesh moving techniques allow us to control mesh resolution near the fluid-structure interfaces so that we can represent the boundary layers more accurately. In the mesh moving techniques we designed, the motion of the nodes is governed by the equations of elasticity, and mesh deformation is handled selectively based on element sizes and deformation modes. This is helping us reduce the frequency of remeshing. With the solid-extension mesh moving technique presented in this paper, we are also able to limit mesh distortion in thin layers of elements placed near fluid-structure interfaces. © 2004 Elsevier B.V. All rights reserved.

[95]

T.E. Tezduyar and S. Sathe, “Enhanced-discretization space-time technique (EDSTT)”, Computer Methods in Applied Mechanics and Engineering, 193 (2004) 1385–1401, 10.1016/j.cma.2003.12.029
@ARTICLE{Tezduyar03a, AUTHOR = {T. E.~Tezduyar and S.~Sathe}, PAGES = {1385--1401}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {193}, TITLE = {Enhanced-Discretization Space-Time Technique {(EDSTT)}}, YEAR = {2004}, DOI = {10.1016/j.cma.2003.12.029} } Abstract:
The enhanced-discretization space-time technique (EDSTT) was developed for the purpose of being able to, in the context of a space-time formulation, enhance the time-discretization in regions of the fluid domain requiring smaller time steps. Such requirements are often encountered in time-accurate computations of fluid-structure interactions, where the time-step size required by the structural dynamics part is smaller, and carrying out the entire computation with that time-step size would be too inefficient for the fluid dynamics part. In the EDSTT-single-mesh (EDSTT-SM) approach, a single space-time mesh, unstructured both in space and time, would be used to enhance the time-discretization in regions requiring smaller time steps. In the EDSTT-multi-mesh (EDSTT-MM) approach, we complement the space-time concept of the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation with the multi-mesh concept of the enhanced-discretization interface-capturing technique (EDICT). In applications to fluid-structure interactions, the structural dynamics modeling is based on a single space-time mesh and the fluid dynamics modeling is based on two space-time meshes. The structural dynamics interface nodes in the space-time domain also belong to the second fluid mesh, which accommodates the time-step requirement of the structural dynamics. We apply the EDSTT-SM and EDSTT-MM approaches to a number of test problems to demonstrate how these methods work and why they would be desirable to use in time-accurate computations. © 2004 Elsevier B.V. All rights reserved.

[94]

K. Stein, T. Tezduyar, and R. Benney, “Computational methods for modeling parachute systems”, Computing in Science and Engineering, 5 (2003) 39–46, 10.1109/MCISE.2003.1166551
@ARTICLE{Stein02e, AUTHOR = {K.~Stein and T.~Tezduyar and R.~Benney}, PAGES = {39--46}, JOURNAL = {Computing in Science and Engineering}, VOLUME = {5}, TITLE = {Computational Methods for Modeling Parachute Systems}, YEAR = {2003}, DOI = {10.1109/MCISE.2003.1166551} } Abstract:
Computational models that predict the aerodynamic performance of parachute systems are discussed. The focus of the discussion was on the challenges involved in developing computational models of airdrop systems and the computational issues that arise, when simulating interactions between parachute structural dynamics and aerodynamics. Deforming-spatial-domain/stabilized space-time formulation and adaptive mesh methods are described.

[93]

T.E. Tezduyar, “Computation of moving boundaries and interfaces and stabilization parameters”, International Journal for Numerical Methods in Fluids, 43 (2003) 555–575, 10.1002/fld.505
@ARTICLE{Tezduyar02a, AUTHOR = {T. E.~Tezduyar}, PAGES = {555--575}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {43}, TITLE = {Computation of Moving Boundaries and Interfaces and Stabilization Parameters}, YEAR = {2003}, DOI = {10.1002/fld.505} } Abstract:
The interface-tracking and interface-capturing techniques we developed in recent years for computation of flow problems with moving boundaries and interfaces rely on stabilized formulations such as the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space-time formulation, where the mesh moves to track the interface. The interface-capturing techniques, typically used with non-moving meshes, are based on a stabilized semi-discrete formulation of the Navier-Stokes equations, combined with a stabilized formulation of the advection equation governing the time-evolution of an interface function marking the interface location. We provide an overview of the interface-tracking and interface-capturing techniques, and highlight how we determine the stabilization parameters used in the stabilized formulations. © 2003 John Wiley and Sons, Ltd.

[92]

J.E. Akin, T. Tezduyar, M. Ungor, and S. Mittal, “Stabilization parameters and Smagorinsky turbulence model”, Journal of Applied Mechanics, 70 (2003) 2–9, 10.1115/1.1526569
@ARTICLE{Akin01a, AUTHOR = {J. E.~Akin and T.~Tezduyar and M.~Ungor and S.~Mittal}, PAGES = {2--9}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {70}, TITLE = {Stabilization Parameters and {S}magorinsky Turbulence Model}, YEAR = {2003}, DOI = {10.1115/1.1526569} } Abstract:
For the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations for flow problems, we present in this paper a comparative study of the stabilization parameters defined in different ways. The stabilization parameters are closely related to the local length scales ("element length"), and our comparisons include parameters defined based on the element-level matrices and vectors, some earlier definitions of element lengths, and extensions of these to higher-order elements. We also compare the numerical viscosities generated by these stabilized formulations with the eddy viscosity associated with a Smagorinsky turbulence model that is based on element length scales.

[91]

K. Stein, T. Tezduyar, and R. Benney, “Mesh moving techniques for fluid–structure interactions with large displacements”, Journal of Applied Mechanics, 70 (2003) 58–63, 10.1115/1.1530635
@ARTICLE{Stein01f, AUTHOR = {K.~Stein and T.~Tezduyar and R.~Benney}, PAGES = {58--63}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {70}, TITLE = {Mesh Moving Techniques for Fluid--Structure Interactions with Large Displacements}, YEAR = {2003}, DOI = {10.1115/1.1530635} } Abstract:
In computation of fluid-structure interactions, we use mesh update methods consisting of mesh-moving and remeshing-as-needed. When the geometries are complex and the structural displacements are large, it becomes even more important that the mesh moving techniques are designed with the objective to reduce the frequency of remeshing. To that end, we present here mesh moving techniques where the motion of the nodes is governed by the equations of elasticity, with selective treatment of mesh deformation based on element sizes as well as deformation modes in terms of shape and volume changes. We also present results from application of these techniques to a set of two-dimensional test cases.

[90]

K. Stein, T. Tezduyar, V. Kumar, S. Sathe, R. Benney, E. Thornburg, C. Kyle, and T. Nonoshita, “Aerodynamic interactions between parachute canopies”, Journal of Applied Mechanics, 70 (2003) 50–57, 10.1115/1.1530634
@ARTICLE{Stein01e, AUTHOR = {K.~Stein and T.~Tezduyar and V.~Kumar and S.~Sathe and R.~Benney and E.~Thornburg and C.~Kyle and T.~Nonoshita}, PAGES = {50--57}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {70}, TITLE = {Aerodynamic Interactions Between Parachute Canopies}, YEAR = {2003}, DOI = {10.1115/1.1530634} } Abstract:
Aerodynamic interactions between parachute canopies can occur when two separate parachutes come close to each other or in a cluster of parachutes. For the case of two separate parachutes, our computational study focuses on the effect of the separation distance on the aerodynamic interactions, and also focuses on the fluid-structure interactions with given initial relative positions. For the aerodynamic interactions between the canopies of a cluster of parachutes, we focus on the effect of varying the number and arrangement of the canopies.

[89]

M. Cruchaga, D. Celentano, and T. Tezduyar, “Computation of mould filling processes with a moving Lagrangian interface technique”, Communications in Numerical Methods in Engineering, 18 (2002) 483–493, 10.1002/cnm.506
@ARTICLE{Cruchaga01b, AUTHOR = {M.~Cruchaga and D.~Celentano and T.~Tezduyar}, PAGES = {483--493}, JOURNAL = {Communications in Numerical Methods in Engineering}, VOLUME = {18}, TITLE = {Computation of Mould Filling Processes with a Moving {L}agrangian Interface Technique}, YEAR = {2002}, DOI = {10.1002/cnm.506} } Abstract:
Computation of non-isothermal flow problems involving moving interfaces is presented. A Lagrangian interface technique, defined in the context of a fixed-mesh finite element formulation for incompressible flows, is employed to update the interface position. A global mass-corrector algorithm is used to accurately enforce the global mass conservation. The Navier-Stokes equations are solved with an improved sub-element integration technique to more accurately account for sudden changes in the fluid properties across the interface. The method described is applied to two mould filling problems. Copyright © 2002 John Wiley and Sons, Ltd.

[88]

H. Johari, K. Stein, and T. Tezduyar, “Impulsively started flow about a rigid parachute canopy”, Journal of Aircraft, 38 (2001) 1102–1109, 10.2514/2.2878
@ARTICLE{Johari01a, AUTHOR = {H.~Johari and K.~Stein and T.~Tezduyar}, PAGES = {1102--1109}, JOURNAL = {Journal of Aircraft}, VOLUME = {38}, TITLE = {Impulsively started flow about a rigid parachute canopy}, YEAR = {2001}, DOI = {10.2514/2.2878} } Abstract:
The temporal evolution of the flowfield in the near wake of a parachute canopy is studied computationally with a finite element method. The canopy is assumed to be rigid and impermeable, and the flow is started impulsively. The separated shear layer surrounding the canopy creates a starting vortex ring. As time evolves, flow instabilities cause the vortex ring to become convoluted and eventually lead to the breakup of the ring. This phase of the flow lasts for approximately 16D/U, where D is the mean projected diameter of the canopy and U is the freestream velocity. After the initial phase, the flow goes through a transition phase before settling into its steady state. In the steady-state phase, the drag and base pressure coefficient become nearly constant. The computed drag coefficient matches very well against experimental data. The steady-state phase is reached after a time period of approximately 45D/U. During the steady-state phase, vortex shedding is observed in the near wake despite the nearly constant drag coefficient.

[87]

K.R. Stein, R.J. Benney, T.E. Tezduyar, J.W. Leonard, and M.L. Accorsi, “Fluid–structure interactions of a round parachute: modeling and simulation techniques”, Journal of Aircraft, 38 (2001) 800–808, 10.2514/2.2864
@ARTICLE{Stein01c, AUTHOR = {K. R.~Stein and R. J.~Benney and T. E.~Tezduyar and J. W.~Leonard and M. L.~Accorsi}, PAGES = {800--808}, JOURNAL = {Journal of Aircraft}, VOLUME = {38}, TITLE = {Fluid--Structure Interactions of a Round Parachute: Modeling and Simulation Techniques}, YEAR = {2001}, DOI = {10.2514/2.2864} } Abstract:
A parallel computational technique is presented for carrying out three-dimensional simulations of parachute fluid-structure interactions, and this technique is applied to simulations of airdrop performance and control phenomena in terminal descent. The technique uses a stabilized space-time formulation of the time-dependent, three-dimensional Navier-Stokes equations of incompressible flows for the fluid dynamics part. Turbulent features of the flow are accounted for by using a zero-equation turbulence model. A finite element formulation derived from the principle of virtual work is used for the parachute structural dynamics. The parachute is represented as a cable-membrane tension structure. Coupling of the fluid dynamics with the structural dynamics is implemented over the fluid-structure interface, which is the parachute canopy surface. Large deformations of the structure require that the fluid dynamics mesh is updated at every time step, and this is accomplished with an automatic mesh.moving method. The parachute used in the application presented here is a standard U.S. Army personnel parachute. © 2001 by the American Institute of Aeronautics and Astronautics, Inc.

[86]

T.E. Tezduyar, “Finite element methods for flow problems with moving boundaries and interfaces”, Archives of Computational Methods in Engineering, 8 (2001) 83–130, 10.1007/BF02897870
@ARTICLE{Tezduyar01a, AUTHOR = {T. E.~Tezduyar}, PAGES = {83--130}, JOURNAL = {Archives of Computational Methods in Engineering}, VOLUME = {8}, TITLE = {Finite Element Methods for Flow Problems with Moving Boundaries and Interfaces}, YEAR = {2001}, DOI = {10.1007/BF02897870} } Abstract:
This paper is an overview of the finite element methods developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) [../] for computation of flow problems with moving boundaries and interfaces. This class of problems include those with free surfaces, two-fluid interfaces, fluid-object and fluid-structure interactions, and moving mechanical components. The methods developed can be classified into two main categories. The interface-tracking methods are based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, where the mesh moves to track the interface, with special attention paid to reducing the frequency of remeshing. The interface-capturing methods, typically used for free-surface and two-fluid flows, are based on the stabilized formulation, over non-moving meshes, of both the flow equations and the advection equation governing the time-evolution of an interface function marking the location of the interface. In this category, when it becomes neccessary to increase the accuracy in representing the interface beyond the accuracy provided by the existing mesh resolution around the interface, the Enhanced-Discretization Interface-Capturing Technique (EDICT) can be used to to accomplish that goal. In development of these two classes of methods, we had to keep in mind the requirement that the methods need to be applicable to 3D problems with complex geometries and that the associated large-scale computations need to be carried out on parallel computing platforms. Therefore our parallel implementations of these methods are based on unstructured grids and on both the distributed and shared memory parallel computing approaches. In addition to these two main classes of methods, a number of other ideas and methods have been developed to increase the scope and accuracy of these two classes of methods. The review of all these methods in our presentation here is supplemented by a number numerical examples from parallel computation of complex, 3D flow problems.

[85]

T. Tezduyar and Y. Osawa, “Fluid–structure interactions of a parachute crossing the far wake of an aircraft”, Computer Methods in Applied Mechanics and Engineering, 191 (2001) 717–726, 10.1016/S0045-7825(01)00311-5
@ARTICLE{Tezduyar01c, AUTHOR = {T.~Tezduyar and Y.~Osawa}, PAGES = {717--726}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {191}, TITLE = {Fluid--Structure Interactions of a Parachute Crossing the Far Wake of an Aircraft}, YEAR = {2001}, DOI = {10.1016/S0045-7825(01)00311-5} } Abstract:
In this paper we describe a computational technique for simulation of the fluid-structure interactions of a parachute crossing the far wake of an aircraft. This technique relies on using the long-wake flow data already computed, in our case, with the Multi-Domain Method (MDM) we developed earlier. The fluid-structure interaction computations are carried out over a domain enclosing the parachute and moving with the payload. This domain functions as one of the subdomains of the MDM designed specifically for the parachute fluid-structure interactions considered here. The boundary conditions for this subdomain are extracted from the long-wake flow data, at locations corresponding to the positions of those boundaries in the subdomain over which the wake flow data were computed. The Navier-Stokes equations of incompressible flows, governing the fluid dynamics, are solved with the Deforming-Spatial- Domain/Stabilized Space-Time (DSD/SST) formulation, which can handle changes in the spatial domain occupied by the fluid. This formulation is coupled to the finite element formulation used for solving the membrane equations governing the structural mechanics of the parachute canopy and the equations governing the mechanics of the suspension lines. The numerical example included demonstrates how the technique described here, functioning as a component of the MDM, enables us to simulate the fluid-structure interactions of a parachute crossing an aircraft wake. © 2001 Elsevier Science B.V. All rights reserved.

[84]

T. Tezduyar and Y. Osawa, “The Multi-Domain Method for computation of the aerodynamics of a parachute crossing the far wake of an aircraft”, Computer Methods in Applied Mechanics and Engineering, 191 (2001) 705–716, 10.1016/S0045-7825(01)00310-3
@ARTICLE{Tezduyar00d, AUTHOR = {T.~Tezduyar and Y.~Osawa}, PAGES = {705--716}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {191}, TITLE = {The {M}ulti-{D}omain {M}ethod for Computation of the Aerodynamics of a Parachute Crossing the Far Wake of an Aircraft}, YEAR = {2001}, DOI = {10.1016/S0045-7825(01)00310-3} } Abstract:
We present the multi-domain method (MDM) for computation of unsteady flow past a cargo aircraft and around a parachute crossing the aircraft's far wake. The base computational methods used here are the stabilized semi-discrete and space-time finite element formulations developed earlier. In the MDM, the computational domain is divided into an ordered sequence of overlapping subdomains. The flow field computed over Subdomain-1, which contains the aircraft, supplies the inflow boundary conditions for Subdomain-2, which is used for computing the long-wake flow. Subdomain-3 contains the parachute, and moves across Subdomain-2. The boundary conditions for Subdomain-3 are extracted from the flow field computed over Subdomain-2, at locations corresponding to the positions of the boundaries of Subdomain-3 as it crosses Subdomain-2. The computation over Subdomain-1, which contains a complex but fixed object, is based on a general-purpose implementation of the semi-discrete formulation. The computation over Subdomain-2, which contains no objects, is based on a special-purpose implementation that exploits the simplicity of the mesh to increase the computational speed. The computation over Subdomain-3, which contains a complex and moving object, is based on a general-purpose implementation of the space-time formulation. With a numerical example, we show that different methods can be brought together in the context of the MDM to address the computational challenges involved in the acrodynamics of a parachute crossing the far wake of an aircraft. © 2001 Elsevier Science B.V. All rights reserved.

[83]

K. Stein, R. Benney, T. Tezduyar, and J. Potvin, “Fluid–structure interactions of a cross parachute: numerical simulation”, Computer Methods in Applied Mechanics and Engineering, 191 (2001) 673–687, 10.1016/S0045-7825(01)00312-7
@ARTICLE{Stein01b, AUTHOR = {K.~Stein and R.~Benney and T.~Tezduyar and J.~Potvin}, PAGES = {673--687}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {191}, TITLE = {Fluid--Structure Interactions of a Cross Parachute: Numerical Simulation}, YEAR = {2001}, DOI = {10.1016/S0045-7825(01)00312-7} } Abstract:
The dynamics of parachutes involves complex interaction between the parachute structure and the surrounding flow field. Accurate representation of parachute systems requires treatment of the problem as a fluid-structure interaction (FSI). In this paper we present the numerical simulations we performed for the purpose of comparison to a series of cross-parachute wind tunnel experiments. The FSI model consists of a 3-D fluid dynamics (FD) solver based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) procedure, a structural dynamics (SD) solver, and a method of coupling the two solvers. These FSI simulations include the prediction of the coupled FD and SD behavior, drag histories, flow fields, structural behavior, and equilibrium geometries for the structure. Comparisons between the numerical results and the wind tunnel data are conducted for three cross-parachute models and at three different wind tunnel flow speeds. © 2001 Published by Elsevier Science B.V.

[82]

M. Cruchaga, D. Celentano, and T. Tezduyar, “A moving Lagrangian interface technique for flow computations over fixed meshes”, Computer Methods in Applied Mechanics and Engineering, 191 (2001) 525–543, 10.1016/S0045-7825(01)00300-0
@ARTICLE{Cruchaga01a, AUTHOR = {M.~Cruchaga and D.~Celentano and T.~Tezduyar}, PAGES = {525--543}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {191}, TITLE = {A Moving {L}agrangian Interface Technique for Flow Computations over Fixed Meshes}, YEAR = {2001}, DOI = {10.1016/S0045-7825(01)00300-0} } Abstract:
In this paper, an enhanced finite element formulation for unsteady incompressible flows with moving interfaces is presented. The weak form of the Navier-Stokes equations, written using a generalized streamline operator technique, is coupled with the movement of the interface between two immiscible fluids defined through an independent moving mesh. The position of the interface is updated using a Lagrangian formulation. In this framework, a global mass conservation corrector algorithm and an enhanced element integration technique are proposed to improve accuracy. The method is applied to a number of test problems with moving interfaces. © 2001 Elsevier Science B.V. All rights reserved.

[81]

S.E. Ray and T.E. Tezduyar, “Fluid–object interactions in interior ballistics”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 363–372, 10.1016/S0045-7825(00)00207-3
@ARTICLE{Ray00a, AUTHOR = {S. E.~Ray and T. E.~Tezduyar}, PAGES = {363--372}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {Fluid--Object Interactions in Interior Ballistics}, YEAR = {2000}, DOI = {10.1016/S0045-7825(00)00207-3} } Abstract:
A fluid-object interaction model for an interior ballistics problem is presented. The fluid is a compressible gas and is modeled using the Deformable-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. The objects can move axially within the model domain, and their motion is determined by the fluid pressure forces and collisions with other objects and rigid boundaries. The model is implemented assuming axisymmetry of the geometry and the flow field. The fluid mesh is composed of structured regions of quadrilateral elements and unstructured regions of triangular elements. The structured elements are used near the surface of the objects in order to better resolve the boundary layer, while the unstructured elements are used elsewhere in the domain. As the objects move, the mesh deformation needed to accommodate these motions takes place only in the unstructured parts of the mesh. Application to an interior ballistics problem is presented and discussed.

[80]

V. Kalro and T.E. Tezduyar, “A parallel 3D computational method for fluid–structure interactions in parachute systems”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 321–332, 10.1016/S0045-7825(00)00204-8
@ARTICLE{Kalro00a, AUTHOR = {V.~Kalro and T. E.~Tezduyar}, PAGES = {321--332}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {A Parallel {3D} Computational Method for Fluid--Structure Interactions in Parachute Systems}, YEAR = {2000}, DOI = {10.1016/S0045-7825(00)00204-8} } Abstract:
We present a parallel finite element computational method for 3D simulation of fluid-structure interactions (FSI) in parachute systems. The flow solver is based on a stabilized finite element formulation applicable to problems involving moving boundaries and governed by the Navier-Stokes equations of incompressible flows. The structural dynamics (SD) solver is based on the total Lagrangian description of motion, with cable and membrane elements. The nonlinear equation system is solved iteratively, with a segregated treatment of the fluid and SD equations. The large linear equation systems that need to be solved at every nonlinear iteration are also solved iteratively. The parallel implementation is accomplished using a message-passing programming environment. As a test case, the method is applied to computation of the equilibrium configuration of an anchored ram-air parachute placed in an air stream.

[79]

T.E. Tezduyar and Y. Osawa, “Finite element stabilization parameters computed from element matrices and vectors”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 411–430, 10.1016/S0045-7825(00)00211-5
@ARTICLE{Tezduyar00a, AUTHOR = {T. E.~Tezduyar and Y.~Osawa}, PAGES = {411--430}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {Finite Element Stabilization Parameters Computed from Element Matrices and Vectors}, YEAR = {2000}, DOI = {10.1016/S0045-7825(00)00211-5} } Abstract:
We propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) formulations. The parameters are computed based on the element-level matrices and vectors, which automatically take into account the local length scales, advection field and the Reynolds number. We describe how we compute these parameters in the context of first a time-dependent advection-diffusion equation and then the Navier-Stokes equations of unsteady incompressible flows.

[78]

T. Tezduyar and Y. Osawa, “Methods for parallel computation of complex flow problems”, Parallel Computing, 25 (1999) 2039–2066, 10.1016/S0167-8191(99)00080-0
@ARTICLE{Tezduyar99a, AUTHOR = {T.~Tezduyar and Y.~Osawa}, PAGES = {2039--2066}, JOURNAL = {Parallel Computing}, VOLUME = {25}, TITLE = {Methods for Parallel Computation of Complex Flow Problems}, YEAR = {1999}, DOI = {10.1016/S0167-8191(99)00080-0} } Abstract:
This paper is an overview of some of the methods developed by the Team for Advanced Flow Simulation and Modeling (TstarAFSM) [../] to support flow simulation and modeling in a number of `Targeted Challenges'. The `Targeted Challenges' include unsteady flows with interfaces, fluid-object and fluid-structure interactions, airdrop systems, and air circulation and contaminant dispersion. The methods developed include special numerical stabilization methods for compressible and incompressible flows, methods for moving boundaries and interfaces, advanced mesh management methods, and multi-domain computational methods. We include in this paper a number of numerical examples from the simulation of complex flow problems.

[77]

A. Johnson and T. Tezduyar, “Methods for 3D computation of fluid-object interactions in spatially-periodic flows”, Computer Methods in Applied Mechanics and Engineering, 190 (2001) 3201–3221, 10.1016/S0045-7825(00)00389-3
@ARTICLE{Johnson00a, AUTHOR = {A.~Johnson and T.~Tezduyar}, PAGES = {3201--3221}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {Methods for {3D} Computation of Fluid-Object Interactions in Spatially-Periodic Flows}, YEAR = {2001}, DOI = {10.1016/S0045-7825(00)00389-3} } Abstract:
We present computational methods for 3D simulation of fluid-object interactions in spatially periodic flows. These methods include a stabilized space-time finite element formulation for incompressible flows with spatial periodicity, automatic mesh generation and update techniques for fluid-object mixtures with spatial periodicity, and parallel implementations. The methods can be applied to uni-periodic (i.e., periodic in one direction), bi-periodic, or tri-periodic flows. The methods are described here in the context of tri-periodic flows with fluid-object interactions, and are applied to the simulation of sedimentation of particles in a fluid. We present several case studies where the results obtained provide notable insight into the behavior of fluid-particle mixtures during sedimentation. © 2001 Elsevier Science B.V. All rights reserved.

[76]

M. Behr and T. Tezduyar, “Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components”, Computer Methods in Applied Mechanics and Engineering, 190 (2001) 3189–3200, 10.1016/S0045-7825(00)00388-1
@ARTICLE{Behr00a, AUTHOR = {M.~Behr and T.~Tezduyar}, PAGES = {3189--3200}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {Shear-Slip Mesh Update in {3D} Computation of Complex Flow Problems with Rotating Mechanical Components}, YEAR = {2001}, DOI = {10.1016/S0045-7825(00)00388-1} } Abstract:
In this paper we present a 3D computational technique for simulation of complex, real-world flow problems with fast-rotating mechanical components. This technique is based on the Deformable-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation. Shear-Slip Mesh Update Method (SSMUM), and an efficient parallel implementation for distributed-memory parallel computing platforms. The DSD/SST formulation was developed earlier for flow problems with moving boundaries and interfaces, including flows with moving mechanical components. The DSD/SST formulation requires, as a companion method, an effective mesh update strategy especially in complex flow problems. The SSMUM was developed to meet the mesh update requirements in simulation of flow problems with fast translations, and recently, with a new version of SSMUM, fast rotations. As an example of the class of challenging simulations that can be carried out by this technique, we present computation of flow around a helicopter with its rotor in motion. © Elsevier Science B.V. All rights reserved.

[75]

T.E. Tezduyar, “CFD methods for three-dimensional computation of complex flow problems”, Journal of Wind Engineering and Industrial Aerodynamics, 81 (1999) 97–116, 10.1016/S0167-6105(99)00011-2
@ARTICLE{Tezduyar98c, AUTHOR = {T. E.~Tezduyar}, PAGES = {97--116}, JOURNAL = {Journal of Wind Engineering and Industrial Aerodynamics}, VOLUME = {81}, TITLE = {{CFD} Methods for Three-dimensional Computation of Complex Flow Problems}, YEAR = {1999}, DOI = {10.1016/S0167-6105(99)00011-2} } Abstract:
This paper provides an overview of some of the CFD methods developed by the Team for Advanced Flow Simulation and Modeling (T(Black star)AFSM) [../]. The paper also provides many examples of three-dimensional flow simulations carried out with these CFD methods and advanced parallel supercomputers. The methods and tools described in this paper include: stabilized finite element formulations; formulations for flows with moving boundaries and interfaces; mesh update methods; iterative solution techniques for large nonlinear equation systems; and parallel implementation of these methods. Our target is to be able to address effectively certain classes of flow simulation problems. These include: unsteady flows with interfaces; fluid-object interactions; fluid-structure interactions; airdrop systems; aerodynamics of complex shapes; and contaminant dispersion. © 1999 Elsevier Science Ltd. All rights reserved.

[74]

T.E. Tezduyar and S. Aliabadi, “EDICT for 3D computation of two-fluid interfaces”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 403–410, 10.1016/S0045-7825(00)00210-3
@ARTICLE{Tezduyar00f, AUTHOR = {T. E.~Tezduyar and S.~Aliabadi}, PAGES = {403--410}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {{EDICT} for {3D} Computation of Two-Fluid Interfaces}, YEAR = {2000}, DOI = {10.1016/S0045-7825(00)00210-3} } Abstract:
We present the 3D implementation and applications of the enhanced-discretization interface-capturing technique (EDICT) in computation of unsteady flows with two-fluid interfaces. In such computations, EDICT can be used as a very effective method, which combines the flexibility and efficiency of interface-capturing techniques with the accuracy provided by enhanced discretization at the interfaces. A stabilized finite element interface-capturing technique is used as the base formulation to solve, over a typically non-moving mesh, the Navier-Stokes equations and an advection equation governing the interface function. To increase the accuracy in modeling the interfaces, we use finite element functions with multiple components at and near the interfaces, with each component coming from a different level of mesh refinement. With its parallel implementation on advanced high-performance computing platforms such as the CRAY T3E, EDICT is a powerful tool for the simulation of a complex, 3D unsteady flow problems with two fluid-interfaces, including free surfaces.

[73]

K. Kashiyama, Y. Ohba, T. Takagi, M. Behr, and T. Tezduyar, “Parallel finite element method utilizing the mode splitting and sigma coordinate for shallow water flows”, Computational Mechanics, 23 (1999) 144–150, 10.1007/s004660050394
@ARTICLE{Kashiyama99a, AUTHOR = {K.~Kashiyama and Y.~Ohba and T.~Takagi and M.~Behr and T.~Tezduyar}, PAGES = {144--150}, JOURNAL = {Computational Mechanics}, VOLUME = {23}, TITLE = {Parallel Finite Element Method Utilizing the Mode Splitting and Sigma Coordinate for Shallow Water Flows}, YEAR = {1999}, DOI = {10.1007/s004660050394} } Abstract:
Parallel finite element method for the analysis of quasi-three dimensional shallow water flow is presented. The mode splitting technique and the sigma coordinate (generalized coordinate) are employed to use parallel computers effectively. Parallel implementation of the unstructured grid-based formulation is carried out on the Hitachi parallel-super computer SR2201. The tidal flow of Tokyo Bay is simulated for a numerical example. The speed-up ratio and the efficiency of the parallelization are investigated. The present method is shown to be a useful and powerful tool for the large scale computation of shallow water flows.

[72]

S. Aliabadi and T.E. Tezduyar, “Stabilized-Finite-Element/Interface-Capturing Technique for parallel computation of unsteady flows with interfaces”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 243–261, 10.1016/S0045-7825(00)00200-0
@ARTICLE{Aliabadi97b, AUTHOR = {S.~Aliabadi and T. E.~Tezduyar}, PAGES = {243--261}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {{S}tabilized-{F}inite-{E}lement/{I}nterface-{C}apturing {T}echnique for Parallel Computation of Unsteady Flows with Interfaces}, YEAR = {2000}, DOI = {10.1016/S0045-7825(00)00200-0} } Abstract:
We present the stabilized-finite-element/interface-capturing (SFE/IC) method developed for parallel computation of unsteady flow problems with two-fluid interfaces and free surfaces. The SFE/IC method involves stabilized formulations, an interface-sharpening technique, and the enforcement of global mass conservation for each fluid. The SFE/IC method has been efficiently implemented on the CRAY T3E parallel supercomputer. A number of 2D test problems are presented to demonstrate how the SFE/IC method works and the accuracy it attains. We also show how the SFE/IC method can be very effectively applied to 3D simulation of challenging flow problems, such as two-fluid interfaces in a centrifuge tube and operational stability of a partially filled tanker truck driving over a bump.

[71]

K. Stein, R. Benney, V. Kalro, T.E. Tezduyar, J. Leonard, and M. Accorsi, “Parachute fluid–structure interactions: 3-D Computation”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 373–386, 10.1016/S0045-7825(00)00208-5
@ARTICLE{Stein98b, AUTHOR = {K.~Stein and R.~Benney and V.~Kalro and T. E.~Tezduyar and J.~Leonard and M.~Accorsi}, PAGES = {373--386}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {190}, TITLE = {Parachute Fluid--Structure Interactions: {3-D} {C}omputation}, YEAR = {2000}, DOI = {10.1016/S0045-7825(00)00208-5} } Abstract:
We present a parallel computational strategy for carrying out 3-D simulations of parachute fluid-structure interaction (FSI), and apply this strategy to a round parachute. The strategy uses a stabilized space-time finite element formulation for the fluid dynamics (FD), and a finite element formulation derived from the principle of virtual work for the structural dynamics (SD). The fluid-structure coupling is implemented over compatible surface meshes in the SD and FD meshes. Large deformations of the structure are handled in the FD mesh by using an automatic mesh moving scheme with remeshing as needed.

[70]

Y. Osawa, V. Kalro, and T. Tezduyar, “Multi-domain parallel computation of wake flows”, Computer Methods in Applied Mechanics and Engineering, 174 (1999) 371–391, 10.1016/S0045-7825(98)00305-3
@ARTICLE{Osawa98a, AUTHOR = {Y.~Osawa and V.~Kalro and T.~Tezduyar}, PAGES = {371--391}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {174}, TITLE = {Multi-Domain Parallel Computation of Wake Flows}, YEAR = {1999}, DOI = {10.1016/S0045-7825(98)00305-3} } Abstract:
We present a new, multi-domain parallel computational method for simulation of unsteady flows involving a primary object, a long wake region and, possibly, a secondary object affected by the wake flow. The method is based on the stabilized finite element formulation of the time-dependent Navier-Stokes equations of incompressible flows. In the multi-domain computational method the entire simulation domain is divided into an ordered sequence of overlapping subdomains. The flow data computed over the leading subdomain is used for specifying the inflow boundary conditions for the next subdomain. The subdomain corresponding to the wake would not involve any objects, hence the mesh constructed over this domain would be structured. A special-purpose finite element implementation for structured meshes is used for the wake domain to achieve much higher computational speeds compared to a general-purpose implementation. We present verification studies for the multi-domain method and special-purpose implementation, followed by two numerical examples. The first example is the wake behavior behind a circular cylinder. The second one is the aerodynamic effect of tip vortices released from a leading wing on a trailing wing placed in the far wake.We present a new, multi-domain parallel computational method for simulation of unsteady flows involving a primary object, a long wake region and, possibly, a secondary object affected by the wake flow. The method is based on the stabilized finite element formulation of the time-dependent Navier-Stokes equations of incompressible flows. In the multi-domain computational method the entire simulation domain is divided into an ordered sequence of overlapping subdomains. The flow data computed over the leading subdomain is used for specifying the inflow boundary conditions for the next subdomain. The subdomain corresponding to the wake would not involve any objects, hence the mesh constructed over this domain would be structured. A special-purpose finite element implementation for structured meshes is used for the wake domain to achieve much higher computational speeds compared to a general-purpose implementation. We present verification studies for the multi-domain method and special-purpose implementation, followed by two numerical examples. The first example is the wake behavior behind a circular cylinder. The second one is the aerodynamic effect of tip vortices released from a leading wing on a trailing wing placed in the far wake.

[69]

A.A. Johnson and T.E. Tezduyar, “Advanced mesh generation and update methods for 3D flow simulations”, Computational Mechanics, 23 (1999) 130–143, 10.1007/s004660050393
@ARTICLE{Johnson99a, AUTHOR = {A. A.~Johnson and T. E.~Tezduyar}, PAGES = {130--143}, JOURNAL = {Computational Mechanics}, VOLUME = {23}, TITLE = {Advanced Mesh Generation and Update Methods for {3D} Flow Simulations}, YEAR = {1999}, DOI = {10.1007/s004660050393} } Abstract:
Advanced mesh generation and update methods for parallel 3D computation of complex flow problems are presented. The complexities of the class of problems targeted include complex geometries, unsteady behavior, and moving boundaries and interfaces, such as those encountered in fluid-object interactions. Parallel 3D simulation of 1000 spheres falling in a liquid-filled tube, and other computations, are presented in this paper to demonstrate the challenges involved in this class of flow problems and the methods developed to address these challenges.

[68]

M. Behr and T. Tezduyar, “The Shear-Slip Mesh Update Method”, Computer Methods in Applied Mechanics and Engineering, 174 (1999) 261–274, 10.1016/S0045-7825(98)00299-0
@ARTICLE{Behr99a, AUTHOR = {M.~Behr and T.~Tezduyar}, PAGES = {261--274}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {174}, TITLE = {The {S}hear-{S}lip {M}esh {U}pdate {M}ethod}, YEAR = {1999}, DOI = {10.1016/S0045-7825(98)00299-0} } Abstract:
The Shear-Slip Mesh Update Method, designed to handle certain classes of flow problems with moving boundaries and interfaces, is presented. Specifically, we focus on problems with large but regular boundary displacements, such as straight-line translation or rotation. These motions are accommodated by using a thin layer of deforming space-time elements, together with limited remeshing without any projection at space-time slab interfaces. As eamples, 2D flow around two counter-rotating squares and 3D flow past a propeller are presented.The Shear-Slip Mesh Update Method, designed to handle certain classes of flow problems with moving boundaries and interfaces, is presented. Specifically, we focus on problems with large but regular boundary displacements, such as straight-line translation or rotation. These motions are accommodated by using a thin layer of deforming space-time elements, together with limited remeshing without any projection at space-time slab interfaces. As examples, 2D flow around two counter-rotating squares and 3D flow past a propeller are presented.

[67]

S. Mittal, S. Aliabadi, and T. Tezduyar, “Parallel computation of unsteady compressible flows with the EDICT”, Computational Mechanics, 23 (1999) 151–157, 10.1007/s004660050395
@ARTICLE{Mittal97b, AUTHOR = {S.~Mittal and S.~Aliabadi and T.~Tezduyar}, PAGES = {151--157}, JOURNAL = {Computational Mechanics}, VOLUME = {23}, TITLE = {Parallel Computation of Unsteady Compressible Flows with The {EDICT}}, YEAR = {1999}, DOI = {10.1007/s004660050395} } Abstract:
Recently, the Enhanced-Discretization Interface-Capturing Technique (EDICT) was introduced for simulation of unsteady flow problems with interfaces such as two-fluid and free-surface flows. The EDICT yields increased accuracy in representing the interface. Here we extend the EDICT to simulation of unsteady viscous compressible flows with boundary/shear layers and shock/expansion waves. The purpose is to increase the accuracy in selected regions of the computational domain. An error indicator is used to identify these regions that need enhanced discretization. Stabilized finite-element formulations are employed to solve the Navier-Stokes equations in their conservation law form. The finite element functions corresponding to enhanced discretization are designed to have two components, with each component coming from a different level of mesh refinement over the same computational domain. The primary component comes from a base mesh. A subset of the elements in this base mesh are identified for enhanced discretization by utilizing the error indicator. A secondary, more refined, mesh is constructed by patching together the second-level meshes generated over this subset of elements, and the second component of the functions comes from this mesh. The subset of elements in the base mesh that form the secondary mesh may change from one time level to other depending on the distribution of the error in the computations.

[66]

I. Guler, M. Behr, and T. Tezduyar, “Parallel finite element computation of free-surface flows”, Computational Mechanics, 23 (1999) 117–123, 10.1007/s004660050391
@ARTICLE{Guler98a, AUTHOR = {I.~Guler and M.~Behr and T.~Tezduyar}, PAGES = {117--123}, JOURNAL = {Computational Mechanics}, VOLUME = {23}, TITLE = {Parallel Finite Element Computation of Free-Surface Flows}, YEAR = {1999}, DOI = {10.1007/s004660050391} } Abstract:
In this paper we present parallel 2D and 3D finite element computation of unsteady, incompressible free-surface flows. The computations are based on the Deformable-Spatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the motion of the free surface. The free-surface height is governed by a kinematic free-surface condition, which is also solved with a stabilized formulation. The meshes consist of triangles in 2D and triangular-based prism elements in 3D. The mesh update is achieved with general or special-purpose mesh moving schemes. As examples, 2D flow past spillway of a dam and 3D flow past a surface-piercing circular cylinder are presented.

[65]

S. Mittal and T. Tezduyar, “A unified finite element formulation for compressible and incompressible flows using augmented conservation variables”, Computer Methods in Applied Mechanics and Engineering, 161 (1998) 229–243, 10.1016/S0045-7825(97)00318-6
@ARTICLE{Mittal98a, AUTHOR = {S.~Mittal and T.~Tezduyar}, PAGES = {229--243}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {161}, TITLE = {A unified finite element formulation for compressible and incompressible flows using augmented conservation variables}, YEAR = {1998}, DOI = {10.1016/S0045-7825(97)00318-6} } Abstract:
A unified approach to computing compressible and incompressible flows is proposed. The governing equation for pressure is selected based on the local Mach number. In the incompressible limit the divergence-free constraint on velocity field determines the pressure, while it is the equation of state that governs the pressure solution for the compressible flows. Stabilized finite element formulations, based on the space-time and semi-discrete methods, with the `augmented' conservation variables are employed. The `augmented' conservation variables consist of the usual conservation variables and pressure as an additional variable. The formulation is applied to various test problems involving steady and unsteady flows over a large range of Mach and Reynolds numbers.A unified approach to computing compressible and incompressible flows is proposed. The governing equation for pressure is selected based on the local Mach number. In the incompressible limit the divergence-free constraint on velocity field determines the pressure, while it is the equation of state that governs solution for the compressible flows. Stabilized finite element formulations, based on the space-time and semi-discrete methods, with the 'augmented' conservation variables are employed. The 'augmented' conservation variables consist of the usual conservation variables and pressure as an additional variable. The formulation is applied to various test problems involving steady and unsteady flows over a large range of Mach and Reynolds numbers.

[64]

T. Tezduyar, S. Aliabadi, and M. Behr, “Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flows with interfaces”, Computer Methods in Applied Mechanics and Engineering, 155 (1998) 235–248, 10.1016/S0045-7825(97)00194-1
@ARTICLE{Tezduyar97c, AUTHOR = {T.~Tezduyar and S.~Aliabadi and M.~Behr}, PAGES = {235--248}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {155}, TITLE = {{E}nhanced-{D}iscretization {I}nterface-{C}apturing {T}echnique ({EDICT}) for Computation of Unsteady Flows with Interfaces}, YEAR = {1998}, DOI = {10.1016/S0045-7825(97)00194-1} } Abstract:
We present the Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flow problems with interfaces, such as two-fluid and free-surface flows. In EDICT, we solve, over a non-moving mesh, the Navier-Stokes equations together with an advection equation governing the evolution of an interface function with two distinct values identifying the two fluids. The starting point for the spatial discretization of these equations are the stabilized finite element formulations which possess good stability and accuracy properties. To increase the accuracy in modeling the interfaces, we use finite element functions corresponding to enhanced discretization at and near the interface. These functions are designed to have multiple components, with each component coming from a different level of mesh refinement over the same computational domain. The primary component of the functions for velocity and pressure comes from the base mesh called Mesh-1. A subset of the elements in Mesh-1 are identified to be at or near the interface, and depending on where the interface is, this subset could change from one time level to another. A Mesh-2 is constructed by patching together the second-level meshes generated over this subset of elements, and the second component of the functions for velocity and pressure comes from Mesh-2. For the interface function, we have a third component coming from a Mesh-3 which is constructed by patching together the third-level meshes generated over a subset of elements in Mesh-2. With parallel computation of the test problems presented here, we demonstrate that the EDICT can be used very effectively to increase the accuracy of the base finite element formulations. © 1998 Elsevier Science S.A.

[63]

N. Nigro, M. Storti, S. Idelsohn, and T. Tezduyar, “Physics based GMRES preconditioner for compressible and incompressible Navier–Stokes equations”, Computer Methods in Applied Mechanics and Engineering, 154 (1998) 203–228, 10.1016/S0045-7825(97)00129-1
@ARTICLE{Nigro98a, AUTHOR = {N.~Nigro and M.~Storti and S.~Idelsohn and T.~Tezduyar}, PAGES = {203--228}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {154}, TITLE = {Physics Based {GMRES} Preconditioner for Compressible and Incompressible {N}avier--{S}tokes Equations}, YEAR = {1998}, DOI = {10.1016/S0045-7825(97)00129-1} } Abstract:
This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations using an SUPG finite element formulation and GMRES implicit solver. During the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of Mach and Reynolds numbers [10,26,37]. On the other hand, SUPG finite element formulation and GMRES implicit solver is one of the most robust combinations to solve state of the art CFD problems [1,6,9,22,29,30,31]. The selection of a good preconditioner and its performance on parallel architecture is another open problem in CFD community. The local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures. Due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Mach and Reynolds numbers, being very suitable for massively parallel computations. Finally, it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning. © 1998 Elsevier Science S.A.

[62]

V. Kalro and T. Tezduyar, “3D computation of unsteady flow past a sphere with a parallel finite element method”, Computer Methods in Applied Mechanics and Engineering, 151 (1998) 267–276, 10.1016/S0045-7825(97)00120-5
@ARTICLE{Kalro98b, AUTHOR = {V.~Kalro and T.~Tezduyar}, PAGES = {267--276}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {151}, TITLE = {{3D} Computation of Unsteady Flow past a Sphere with a Parallel Finite Element Method}, YEAR = {1998}, DOI = {10.1016/S0045-7825(97)00120-5} } Abstract:
We present parallel computation of 3D, unsteady, incompressible flow past a sphere. The Navier-Stokes equations of incompressible flows are solved using a stabilized finite element formulation. Equal-order interpolation functions are used for velocity and pressure. The second-order accurate time-marching within the solution process is carried out in an implicit fashion. The coupled, nonlinear equations generated at each time step are solved using an element-vector-based iteration technique. The computed value of the primary frequency associated with vortex shedding is in close agreement with experimental measurements. The computation was performed on the Thinking Machines CM-5.

[61]

S.E. Ray, G.P. Wren, and T.E. Tezduyar, “Parallel implementations of a finite element formulation for fluid–structure interactions in interior flows”, Parallel Computing, 23 (1997) 1279–1292, 10.1016/S0167-8191(97)00053-7
@ARTICLE{Ray97a, AUTHOR = {S. E.~Ray and G. P.~Wren and T. E.~Tezduyar}, PAGES = {1279--1292}, JOURNAL = {Parallel Computing}, VOLUME = {23}, TITLE = {Parallel Implementations of a Finite Element Formulation for Fluid--Structure Interactions in Interior Flows}, YEAR = {1997}, DOI = {10.1016/S0167-8191(97)00053-7} } Abstract:
In this paper, shared-memory parallel implementations of a finite element formulation for unsteady interior flows with fluid-structure interactions are presented. The parallel computing platforms targeted are the CRAY C90, the Silicon Graphics (SGI) ONYX and the SGI Power Challenge. The formulation is based on the stabilized space-time finite element method developed earlier for a more general class of flow problems involving moving boundaries and interfaces. The specific test problem used in the performance evaluations involves fluid-structure interactions between a barotropic working fluid and one of the two pistons surrounding this fluid. We demonstrate that advanced formulations applicable to complex problems can be implemented in a parallel computing environment without resulting in a significant distraction from the scientific objectives of solving such complex problems. © 1997 Elsevier Science B.V.

[60]

T. Tezduyar, V. Kalro, and W. Garrard, “Parallel computational methods for 3D simulation of a parafoil with prescribed shape changes”, Parallel Computing, 23 (1997) 1349–1363, 10.1016/S0167-8191(97)00057-4
@ARTICLE{Tezduyar97e, AUTHOR = {T.~Tezduyar and V.~Kalro and W.~Garrard}, PAGES = {1349--1363}, JOURNAL = {Parallel Computing}, VOLUME = {23}, TITLE = {Parallel Computational Methods for {3D} Simulation of a Parafoil with Prescribed Shape Changes}, YEAR = {1997}, DOI = {10.1016/S0167-8191(97)00057-4} } Abstract:
In this paper we describe parallel computational methods for 3D simulation of the dynamics and fluid dynamics of a parafoil with prescribed, time-dependent shape changes. The mathematical model is based on the time-dependent, 3D Navier-Stokes equations governing the incompressible flow around the parafoil and Newton's law of motion governing the dynamics of the parafoil, with the aerodynamic forces acting on the parafoil calculated from the flow field. The computational methods developed for these 3D simulations include a stabilized space-time finite element formulation to accommodate for the shape changes, special mesh generation and mesh moving strategies developed for this purpose, iterative solution techniques for the large, coupled nonlinear equation systems involved, and parallel implementation of all these methods on scalable computing systems such as the Thinking Machines CM-5. As an example, we report 3D simulation of a flare maneuver in which the parafoil velocity is reduced by pulling down the flaps. This simulation requires solution of over 3.6 million coupled, nonlinear equations at every time step of the simulation. © 1997 Elsevier Science B.V.

[59]

V. Kalro and T. Tezduyar, “Parallel 3D computation of unsteady flows around circular cylinders”, Parallel Computing, 23 (1997) 1235–1248, 10.1016/S0167-8191(97)00050-1
@ARTICLE{Kalro97b, AUTHOR = {V.~Kalro and T.~Tezduyar}, PAGES = {1235--1248}, JOURNAL = {Parallel Computing}, VOLUME = {23}, TITLE = {Parallel {3D} Computation of Unsteady Flows around Circular Cylinders}, YEAR = {1997}, DOI = {10.1016/S0167-8191(97)00050-1} } Abstract:
In this article we present parallel 3D finite element computation of unsteady incompressible flows around circular cylinders. We employ stabilized finite element formulations to solve the Navier-Stokes equations on a thinking machine CM-5 supercomputer. The time integration is based on an implicit method, and the coupled, nonlinear equations generated every time step are solved iteratively, with an element-vector based evaluation technique. This strategy enables us to carry out these computations with millions of coupled, nonlinear equations, and thus resolve the flow features in great detail. At Reynolds number 300 and 800, our results indicate strong 3D features arising from the instability of the columnar vortices forming the Karman street. At Re = 10 000 we employ a large eddy simulation (LES) turbulence model. © 1997 Elsevier Science B.V.

[58]

K. Kashiyama, K. Saitoh, M. Behr, and T.E. Tezduyar, “Parallel finite element methods for large-scale computation of storm surges and tidal flows”, International Journal for Numerical Methods in Fluids, 24 (1997) 1371–1389, 10.1002/(SICI)1097-0363(199706)24:12<1371::AID-FLD565>3.0.CO;2-7
@ARTICLE{Kashiyama96b, AUTHOR = {K.~Kashiyama and K.~Saitoh and M.~Behr and T. E.~Tezduyar}, PAGES = {1371--1389}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {24}, TITLE = {Parallel Finite Element Methods for Large-Scale Computation of Storm Surges and Tidal Flows}, YEAR = {1997}, DOI = {10.1002/(SICI)1097-0363(199706)24:12<1371::AID-FLD565>3.0.CO;2-7} } Abstract:
Massively parallel finite element methods for large-scale computation of storm surges and tidal flows are discussed here. The finite element computations, carried out using unstructured grids, are based on a three-step explicit formulation and on an implicit space-time formulation. Parallel implementations of these unstructured grid-based formulations are carried out on the Fujitsu Highly Parallel Computer AP1000 and on the Thinking Machines CM-5. Simulations of the storm surge accompanying the Ise-Bay typhoon in 1959 and of the tidal flow in Tokyo Bay serve as numerical examples. The impact of parallelization on this type of simulation is also investigated. The present methods are shown to be useful and powerful tools for the analysis of storm surges and tidal flows. © 1997 by John Wiley & Sons, Ltd.

[57]

A.A. Johnson and T.E. Tezduyar, “3D simulation of fluid-particle interactions with the number of particles reaching 100”, Computer Methods in Applied Mechanics and Engineering, 145 (1997) 301–321, 10.1016/S0045-7825(96)01223-6
@ARTICLE{Johnson97a, AUTHOR = {A. A.~Johnson and T. E.~Tezduyar}, PAGES = {301--321}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {145}, TITLE = {{3D} Simulation of Fluid-Particle Interactions with the Number of Particles Reaching 100}, YEAR = {1997}, DOI = {10.1016/S0045-7825(96)01223-6} } Abstract:
A high performance computing research tool has been developed for 3D simulation of fluid-particle interactions with the number of particles reaching 100. The tool is based on a stabilized space-time finite element formulation for moving boundaries and interfaces and parallel computing. Other components of this tool include: fast automatic mesh generation with structured layers of elements around the particles and unstructured meshes elsewhere; an automatic mesh moving method combined with remeshing as needed; accurate and efficient projection of the solution between the old and new meshes after each remesh; surface mesh refinement as two spheres or a sphere and the tube wall get close; and multi-platform computing. We apply this tool to the simulation of two cases involving 101 spheres falling in a liquid-filled tube. In both cases the initial distribution of the spheres in the tube is random. In the first simulation the size of the spheres is also random, whereas in the second case it is uniform. We demonstrate that the tool developed can be used for simulation of this class of problems with computing durations kept at acceptable levels.

[56]

T. Tezduyar, S. Aliabadi, M. Behr, A. Johnson, V. Kalro, and M. Litke, “Flow simulation and high performance computing”, Computational Mechanics, 18 (1996) 397–412, 10.1007/BF00350249
@ARTICLE{Tezduyar96b, AUTHOR = {T.~Tezduyar and S.~Aliabadi and M.~Behr and A.~Johnson and V.~Kalro and M.~Litke}, PAGES = {397--412}, JOURNAL = {Computational Mechanics}, VOLUME = {18}, TITLE = {Flow Simulation and High Performance Computing}, YEAR = {1996}, DOI = {10.1007/BF00350249} } Abstract:
Flow simulation is a computational tool for exploring science and technology involving flow applications. It can provide cost-effective alternatives or complements to laboratory experiments, field tests and prototyping. Flow simulation relies heavily on high performance computing (HPC). We view HPC as having two major components. One is advanced algorithms capable of accurately simulating complex, real-world problems. The other is advanced computer hardware and networking with sufficient power, memory and bandwidth to execute those simulations. While HPC enables flow simulation, flow simulation motivates development of novel HPC techniques. This paper focuses on demonstrating that flow simulation has come a long way and is being applied to many complex, real-world problems in different fields of engineering and applied sciences, particularly in aerospace engineering and applied fluid mechanics. Flow simulation has come a long way because HPC has come a long way. This paper also provides a brief review of some of the recently-developed HPC methods and tools that has played a major role in bringing flow simulation where it is today. A number of 3D flow simulations are presented in this paper as examples of the level of computational capability reached with recent HPC methods and hardware. These examples are, flow around a fighter aircraft, flow around two trains passing in a tunnel, large ram-air parachutes, flow over hydraulic structures, contaminant dispersion in a model subway station, airflow past an automobile, multiple spheres falling in a liquid-filled tube, and dynamics of a paratrooper jumping from a cargo aircraft.

[55]

G.P. Wren, S.E. Ray, S.K. Aliabadi, and T.E. Tezduyar, “Simulation of flow problems with moving mechanical components, fluid–structure interactions and two-fluid interfaces”, International Journal for Numerical Methods in Fluids, 24 (1997) 1433–1448, 10.1002/(SICI)1097-0363(199706)24:12<1433::AID-FLD568>3.3.CO;2-L
@ARTICLE{Wren97a, AUTHOR = {G. P.~Wren and S. E.~Ray and S. K.~Aliabadi and T. E.~Tezduyar}, PAGES = {1433--1448}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {24}, TITLE = {Simulation of Flow Problems with Moving Mechanical Components, Fluid--Structure Interactions and Two-Fluid Interfaces}, YEAR = {1997}, DOI = {10.1002/(SICI)1097-0363(199706)24:12<1433::AID-FLD568>3.3.CO;2-L} }

[54]

W.B. Sturek, S. Ray, S. Aliabadi, C. Waters, and T.E. Tezduyar, “Parallel finite element computation of missile aerodynamics”, International Journal for Numerical Methods in Fluids, 24 (1997) 1417–1432, 10.1002/(SICI)1097-0363(199706)24:12<1417::AID-FLD567>3.3.CO;2-E
@ARTICLE{Sturek97a, AUTHOR = {W. B.~Sturek and S.~Ray and S.~Aliabadi and C.~Waters and T. E.~Tezduyar}, PAGES = {1417--1432}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {24}, TITLE = {Parallel Finite Element Computation of Missile Aerodynamics}, YEAR = {1997}, DOI = {10.1002/(SICI)1097-0363(199706)24:12<1417::AID-FLD567>3.3.CO;2-E} }

[53]

V. Kalro, S. Aliabadi, W. Garrard, T. Tezduyar, S. Mittal, and K. Stein, “Parallel finite element simulation of large ram-air parachutes”, International Journal for Numerical Methods in Fluids, 24 (1997) 1353–1369, 10.1002/(SICI)1097-0363(199706)24:12<1353::AID-FLD564>3.0.CO;2-6
@ARTICLE{Kalro96a, AUTHOR = {V.~Kalro and S.~Aliabadi and W.~Garrard and T.~Tezduyar and S.~Mittal and K.~Stein}, PAGES = {1353--1369}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {24}, TITLE = {Parallel Finite Element Simulation of Large Ram-Air Parachutes}, YEAR = {1997}, DOI = {10.1002/(SICI)1097-0363(199706)24:12<1353::AID-FLD564>3.0.CO;2-6} } Abstract:
In the near future, large ram-air parachutes are expected to provide the capability of delivering 21 ton pay loads from altitudes as high as 25,000 ft. In development and test and evaluation of these parachutes the size of the parachute needed and the deployment stages involved make high-performance computing (HPC) simulations a desirable alternative to costly airdrop tests. Although computational simulations based on realistic, 3D, time-dependent models will continue to be a major computational challenge, advanced finite element simulation techniques recently developed for this purpose and the execution of these techniques on HPC platforms are significant steps in the direction to meet this challenge. In this paper, two approaches for analysis of the inflation and gliding of ram-air parachutes are presented. In one of the approaches the point mass flight mechanics equations are solved with the time-varying drag and lift areas obtained from empirical data. This approach is limited to parachutes with similar configurations to those for which data are available. The other approach is 3D finite element computations based on the Navier-Stokes equations governing the airflow around the parachute canopy and Newton's law of motion governing the 3D dynamics of the canopy, with the forces acting on the canopy calculated from the simulated flow field. At the earlier stages of canopy inflation the parachute is modelled as an expanding box, whereas at the later stages, as it expands, the box transforms to a parafoil and glides. These finite element computations are carried out on the massively parallel supercomputers CRAY T3D and Thinking Machines CM-5, typically with millions of coupled, non-linear finite element equations solved simultaneously at every time step or pseudo-time step of the simulation. © 1997 by John Wiley & Sons, Ltd.

[52]

A.A. Johnson and T.E. Tezduyar, “Parallel computation of incompressible flows with complex geometries”, International Journal for Numerical Methods in Fluids, 24 (1997) 1321–1340, 10.1002/(SICI)1097-0363(199706)24:12<1321::AID-FLD562>3.3.CO;2-C
@ARTICLE{Johnson96b, AUTHOR = {A. A.~Johnson and T. E.~Tezduyar}, PAGES = {1321--1340}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {24}, TITLE = {Parallel Computation of Incompressible Flows with Complex Geometries}, YEAR = {1997}, DOI = {10.1002/(SICI)1097-0363(199706)24:12<1321::AID-FLD562>3.3.CO;2-C} } Abstract:
We present our numerical methods for the solution of large-scale incompressible flow applications with complex geometries. These methods include a stabilized finite element formulation of the Navier-Stokes equations, implementation of this formulation on parallel architectures such as the Thinking Machines CM-5 and the CRAY T3D, and automatic 3D mesh generation techniques based on Delaunay-Voronoï methods for the discretization of complex domains. All three of these methods are required for the numerical simulation of most engineering applications involving fluid flow. We apply these methods to the simulation of airflow past an automobile and fluid-particle interactions. The simulation of airflow past an automobile is of very large scale with a high level of detail and yielded many interesting airflow patterns which help in understanding the aerodynamic characteristics of such vehicles. © 1997 by John Wiley & Sons, Ltd.

[51]

A.A. Johnson and T.E. Tezduyar, “Simulation of multiple spheres falling in a liquid-filled tube”, Computer Methods in Applied Mechanics and Engineering, 134 (1996) 351–373, 10.1016/0045-7825(95)00988-4
@ARTICLE{Johnson96a, AUTHOR = {A. A.~Johnson and T. E.~Tezduyar}, PAGES = {351--373}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {134}, TITLE = {Simulation of Multiple Spheres Falling in a Liquid-Filled Tube}, YEAR = {1996}, DOI = {10.1016/0045-7825(95)00988-4} } Abstract:
A new 3D finite element flow simulation capability for fluid-particle interactions is presented and applied to study time-dependent behavior of multiple spheres falling in a liquid-filled tube. This capability is based on the flow simulation strategies such as stabilized space-time formulation for moving boundaries and interfaces, automatic mesh generation with structured layers of elements around the spheres, automatic mesh moving with remesh only as needed, and the implementation of these strategies on massively parallel computing platforms. Several cases of multiple spheres falling in a liquid-filled tube are studied, with the number of spheres ranging from two to five. In all cases, depending on the number of spheres and their initial arrangement, a stable state is eventually reached with all spheres arranged in a pattern corresponding to that stable state, and with all of them falling with the same terminal velocity.

[50]

M. Behr, D. Hastreiter, S. Mittal, and T.E. Tezduyar, “Incompressible flow past a circular cylinder: dependence of the computed flow field on the location of the lateral boundaries”, Computer Methods in Applied Mechanics and Engineering, 123 (1995) 309–316, 10.1016/0045-7825(94)00736-7
@ARTICLE{Behr95a, AUTHOR = {M.~Behr and D.~Hastreiter and S.~Mittal and T. E.~Tezduyar}, PAGES = {309--316}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {123}, TITLE = {Incompressible Flow Past a Circular Cylinder: Dependence of the Computed Flow Field on the Location of the Lateral Boundaries}, YEAR = {1995}, DOI = {10.1016/0045-7825(94)00736-7} } Abstract:
The influence of the location of the lateral boundaries on 2D computation of unsteady incompressible flow past a circular cylinder is investigated. The case of Reynolds number 100 is used as a benchmark, and several quantities characterizing the unsteady flow are obtained for a range of lateral boundary locations. The computations are performed with two distinct finite element formulations - space-time velocity-pressure formulation and velocity-pressure-stress formulation. We conclude that the distance between the cylinder and the lateral boundaries can have a significant effect on the Strouhal number and other flow quantities. The minimum distance at which this influence vanishes has been found to be larger than what is commonly assumed. © 1995.

[49]

K. Kashiyama, H. Ito, M. Behr, and T. Tezduyar, “Three-step explicit finite element computation of shallow water flows on a massively parallel computer”, International Journal for Numerical Methods in Fluids, 21 (1995) 885–900, 10.1002/fld.1650211009
@ARTICLE{Kashiyama94b, AUTHOR = {K.~Kashiyama and H.~Ito and M.~Behr and T.~Tezduyar}, PAGES = {885--900}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {21}, TITLE = {Three-step Explicit Finite Element Computation of Shallow Water Flows on a Massively Parallel Computer}, YEAR = {1995}, DOI = {10.1002/fld.1650211009} } Abstract:
Massively parallel finite element strategies for large‐scale computations of shallow water flows and contaminant transport are presented. The finite element discretizations, carried out on unstructured grids, are based on a three‐step explicit formulation both for the shallow water equations and for the advection‐diffusion equation governing the contaminant transport. Parallel implementations of these unstructured‐grid‐based formulations are carried out on the Army High Performance Computing Research Center Connection Machine CM‐5. It is demonstrated with numerical examples that the strategies presented are applicable to large‐scale computations of various shallow water flow problems. Copyright © 1995 John Wiley & Sons, Ltd

[48]

S.K. Aliabadi and T.E. Tezduyar, “Parallel fluid dynamics computations in aerospace applications”, International Journal for Numerical Methods in Fluids, 21 (1995) 783–805, 10.1002/fld.1650211003
@ARTICLE{Aliabadi94b, AUTHOR = {S. K.~Aliabadi and T. E.~Tezduyar}, PAGES = {783--805}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {21}, TITLE = {Parallel Fluid Dynamics Computations in Aerospace Applications}, YEAR = {1995}, DOI = {10.1002/fld.1650211003} } Abstract:
Massively parallel finite element computations of the compressible Euler and Navier‐Stokes equations using parallel supercomputers are presented. The finite element formulations are based on the conservation variables and the streamline‐upwind/Petrov‐Galerkin (SUPG) stabilization method is used to prevent potential numerial oscillations due to dominant advection terms. These computations are based on both implicit and explicit methods and their parallel implementation assumes that the mesh is unstructured. The implicit computations are based on iterative strategies. Large‐scale 3D problems are solved using a matrix‐free iteration technique which reduces the memory requirements significantly. The flow problems we consider typically come from aerospace applications, including those in 3D and those involving moving boundaries interacting with boundary layers and shocks. Problems with fixed boundaries are solved using a semidiscrete formulation and the ones involving moving boundaries are solved using the deformable‐spatial‐domain/stabilized‐space‐time (DSD/SST) formulation. Copyright © 1995 John Wiley & Sons, Ltd

[47]

S. Mittal and T.E. Tezduyar, “Parallel finite element simulation of 3D incompressible flows: Fluid-structure interactions”, International Journal for Numerical Methods in Fluids, 21 (1995) 933–953, 10.1002/fld.1650211011
@ARTICLE{Mittal94c, AUTHOR = {S.~Mittal and T. E.~Tezduyar}, PAGES = {933--953}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {21}, TITLE = {Parallel Finite Element Simulation of 3{D} Incompressible Flows: {F}luid-Structure Interactions}, YEAR = {1995}, DOI = {10.1002/fld.1650211011} } Abstract:
Massively parallel finite element computations of 3D, unsteady incompressible flows, including those involving fluid‐structure interactions, are presented. The computation with time‐varying spatial domains are based on the deforming spatial domain/stabilized space‐time (DSD/SST) finite element formulation. The capability to solve 3D problems involving fluid‐structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Computations of flow past a stationary rectangular wing at Reynolds number 1000, 2500 and 107 reveal interesting flow patterns. In these computations, at each time step approximately 3 × 106 non‐linear equations are solved to update the flow field. Also, preliminary results are presented for flow past a wing in flapping motion. In this case a specially designed mesh moving scheme is employed to eliminate the need for remeshing. All these computations are carried out on the Army High Performance Computing Research Center supercomputers CM‐200 and CM‐5, with major speed‐ups compared with traditional supercomputers. The coupled equation systems arising from the finite element discretizations of these large‐scale problems are solved iteratively with diagonal preconditioners. In some cases, to reduce the memory requirements even further, these iterations are carried out with a matrix‐free strategy. The finite element formulations and their parallel implementations assume unstructured meshes. Copyright © 1995 John Wiley & Sons, Ltd

[46]

G.P. Wren, S.E. Ray, S.K. Aliabadi, and T.E. Tezduyar, “Space–time finite element computation of compressible flows between moving components”, International Journal for Numerical Methods in Fluids, 21 (1995) 981–991, 10.1002/fld.1650211015
@ARTICLE{Wren95a, AUTHOR = {G. P.~Wren and S. E.~Ray and S. K.~Aliabadi and T. E.~Tezduyar}, PAGES = {981--991}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {21}, TITLE = {Space--Time Finite Element Computation of Compressible Flows Between Moving Components}, YEAR = {1995}, DOI = {10.1002/fld.1650211015} } Abstract:
A numerical simulation capability for the injector flow of a regenerative liquid propellant gun (RLPG) is presented. The problem involves fairly complex geometries and two pistons in relative motion; therefore a stabilized space‐time finite element formulation developed earlier and capable of handling flows with moving mechanical components is used. In addition to the specifics of the numerical method, its application to a 30 mm RLPG test firing is discussed. The computational data from the simulation of this test case are interpreted to provide information on flow characteristics, with emphasis on the tendency of the flow to separate from the injection orifice boundary of the test problem. In addition, the computations provided insight into the behaviour of the flow entering the combustion chamber. Copyright © 1995 John Wiley & Sons, Ltd

[45]

A.A. Johnson and T.E. Tezduyar, “Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces”, Computer Methods in Applied Mechanics and Engineering, 119 (1994) 73–94, 10.1016/0045-7825(94)00077-8
@ARTICLE{Johnson94a, AUTHOR = {A. A.~Johnson and T. E.~Tezduyar}, PAGES = {73--94}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {119}, TITLE = {Mesh Update Strategies in Parallel Finite Element Computations of Flow Problems with Moving Boundaries and Interfaces}, YEAR = {1994}, DOI = {10.1016/0045-7825(94)00077-8} } Abstract:
We present strategies to update the mesh as the spatial domain changes its shape in computations of flow problems with moving boundaries and interfaces. These strategies are used in conjunction with the stabilized space-time finite element formulations introduced earlier for computation of flow problems with free surfaces, two-liquid interfaces, moving mechanical components, and fluid-structure and fluid-particle interactions. In these mesh update strategies, based on the special and automatic mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors and to minimize the cost associated with mesh generation and parallelization set-up. These costs could otherwise become overwhelming in 3D problems. We present several examples of these mesh update strategies being used in massively parallel computation of incompressible flow problems. © 1994.

[44]

J.G. Kennedy, M. Behr, V. Kalro, and T.E. Tezduyar, “Implementation of implicit finite element methods for incompressible flows on the CM-5”, Computer Methods in Applied Mechanics and Engineering, 119 (1994) 95–111, 10.1016/0045-7825(94)00078-6
@ARTICLE{Kennedy94a, AUTHOR = {J. G.~Kennedy and M.~Behr and V.~Kalro and T. E.~Tezduyar}, PAGES = {95--111}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {119}, TITLE = {Implementation of Implicit Finite Element Methods for Incompressible Flows on the {CM}-5}, YEAR = {1994}, DOI = {10.1016/0045-7825(94)00078-6} } Abstract:
A parallel implementation of an implicit finite element formulation for incompressible fluids on a distributed-memory massively parallel computer is presented. The dominant issue that distinguishes the implementation of finite element problems on distributed-memory computers from that on traditional shared-memory scalar or vector computers is the distribution of data (and hence workload) to the processors and the non-uniform memory hierarchy associated with the processors, particularly the non-uniform costs associated with on-processor and off-processor memory references. Accessing data stored in a remote processor requires computing resources an order of magnitude greater than accessing data locally in a processor. This distribution of data motivates the development of alternatives to traditional algorithms and data structures designed for shared-memory computers, which must now account for distributed-memory architectures. Data structures as well as data decomposition and data communication algorithms designed for distributed-memory computers are presented in the context of high level language constructs from High Performance Fortran. The discussion relies primarily on abstract features of the hardware and software environment and should be applicable, in principle, to a variety of distributed-memory system. The actual implementation is carried out on a Connection Machine CM-5 system with high performance communication functions. © 1994.

[43]

T.E. Tezduyar, S.K. Aliabadi, M. Behr, and S. Mittal, “Massively parallel finite element simulation of compressible and incompressible flows”, Computer Methods in Applied Mechanics and Engineering, 119 (1994) 157–177, 10.1016/0045-7825(94)00082-4
@ARTICLE{Tezduyar94b, AUTHOR = {T. E.~Tezduyar and S. K.~Aliabadi and M.~Behr and S.~Mittal}, PAGES = {157--177}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {119}, TITLE = {Massively Parallel Finite Element Simulation of Compressible and Incompressible Flows}, YEAR = {1994}, DOI = {10.1016/0045-7825(94)00082-4} } Abstract:
We present a review of where our research group stands in parallel finite element simulation of flow problems on the Connection Machines, an effort that started for our group in the fourth quarter of 1991. This review includes an overview of our work on computation of flow problems involving moving boundaries and interfaces, such as free surfaces, two-liquid interfaces, and fluid-structure and fluid-particle interactions. With numerous examples, we demonstrate that, with these new computational capabilities, today we are at a point where we routinely solve practical flow problems, including those in 3D and those involving moving boundaries and interfaces. We solve these problems with unstructured grids and implicit methods, with some of the problem sizes exceeding 5 000 000 equations, and with computational speeds up to two orders of magnitude higher than what was previously available to us on the traditional vector supercomputers. © 1994.

[42]

T. Tezduyar, S. Aliabadi, M. Behr, A. Johnson, and S. Mittal, “Parallel finite-element computation of 3D flows”, Computer, 26 (1993) 27–36, 10.1109/2.237441
@ARTICLE{Tezduyar93a, AUTHOR = {T.~Tezduyar and S.~Aliabadi and M.~Behr and A.~Johnson and S.~Mittal}, PAGES = {27--36}, JOURNAL = {Computer}, VOLUME = {26}, TITLE = {Parallel Finite-Element Computation of {3D} Flows}, YEAR = {1993}, DOI = {10.1109/2.237441}, NUMBER = {10} }

[41]

S. Mittal and T.E. Tezduyar, “Massively parallel finite element computation of incompressible flows involving fluid-body interactions”, Computer Methods in Applied Mechanics and Engineering, 112 (1994) 253–282, 10.1016/0045-7825(94)90029-9
@ARTICLE{Mittal94a, AUTHOR = {S.~Mittal and T. E.~Tezduyar}, PAGES = {253--282}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {112}, TITLE = {Massively Parallel Finite Element Computation of Incompressible Flows Involving Fluid-Body Interactions}, YEAR = {1994}, DOI = {10.1016/0045-7825(94)90029-9} } Abstract:
We describe our massively parallel finite element computations of unsteady incompressible flows involving fluid-body interactions. These computations are based on the Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) finite element formulation. Unsteady flows past a stationary NACA 0012 airfoil are computed for Reynolds numbers 1000, 5000 and 100 000. Significantly different flow patterns are observed for these three cases. The method is then applied to computation of the dynamics of an airfoil falling in a viscous fluid under the influence of gravity. It is observed that the location of the center of gravity of the airfoil plays an important role in determining its pitch stability. Computations are reported also for simulation of the dynamics of a two-dimensional 'projectile' that has a certain initial velocity. Specially designed mesh moving schemes are employed to eliminate the need for remeshing. All these computations were carried out on the Thinking Machines CM-200 and CM-5 supercomputers, with major speed-ups compared to traditional supercomputers. The implicit equation systems arising from the finite element discretizations of these large-scale problems are solved iteratively by using the GMRES update technique with diagonal preconditioners. The finite element formulations and their parallel implementations assume unstructured meshes. © 1994.

[40]

M. Behr and T.E. Tezduyar, “Finite element solution strategies for large-scale flow simulations”, Computer Methods in Applied Mechanics and Engineering, 112 (1994) 3–24, 10.1016/0045-7825(94)90016-7
@ARTICLE{Behr92d, AUTHOR = {M.~Behr and T. E.~Tezduyar}, PAGES = {3--24}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {112}, TITLE = {Finite Element Solution Strategies for Large-Scale Flow Simulations}, YEAR = {1994}, DOI = {10.1016/0045-7825(94)90016-7} } Abstract:
Large-scale flow simulation strategies involving implicit finite element formulations are described in the context of incompressible flows. The stabilized space-time formulation for problems involving moving boundaries and interfaces is presented, followed by a discussion of mesh moving schemes. The methods of solution of large linear systems of equations are reviewed, and an implementation of the entire finite element code, permitting the use of totally unstructured meshes, on a massively parallel supercomputer is considered. As an example, this methodology is applied to a flow problem involving three-dimensional simulation of liquid sloshing in a tank subjected to vertical vibrations. © 1994.

[39]

M. Behr, A. Johnson, J. Kennedy, S. Mittal, and T. Tezduyar, “Computation of incompressible flows with implicit finite element implementations on the Connection Machine”, Computer Methods in Applied Mechanics and Engineering, 108 (1993) 99–118, 10.1016/0045-7825(93)90155-Q
@ARTICLE{Behr92b, AUTHOR = {M.~Behr and A.~Johnson and J.~Kennedy and S.~Mittal and T.~Tezduyar}, PAGES = {99--118}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {108}, TITLE = {Computation of Incompressible Flows with Implicit Finite Element Implementations on the {C}onnection {M}achine}, YEAR = {1993}, DOI = {10.1016/0045-7825(93)90155-Q} } Abstract:
Two implicit finite element formulations for incompressible flows have been implemented on the Connection Machine supercomputers and successfully applied to a set of time-dependent problems. The stabilized space-time formulation for moving boundaries and interfaces, and a new stabilized velocity-pressure-stress formulation are both described, and significant aspects of the implementation of these methods on massively parallel architectures are discussed. Several numerical results for flow problems involving moving as well as fixed cylinders and airfoils are reported. The parallel implementation, taking full advantage of the computational speed of the new generation of supercomputers, is found to be a significant asset in fluid dynamics research. Its current capability to solve large-scale problems, especially when coupled with the potential for growth enjoyed by massively parallel computers, make the implementation a worthwhile enterprise. © 1993.

[38]

S.K. Aliabadi and T.E. Tezduyar, “Space–time finite element computation of compressible flows involving moving boundaries and interfaces”, Computer Methods in Applied Mechanics and Engineering, 107 (1993) 209–223, 10.1016/0045-7825(93)90176-X
@ARTICLE{Aliabadi92a, AUTHOR = {S. K.~Aliabadi and T. E.~Tezduyar}, PAGES = {209--223}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {107}, TITLE = {Space--Time Finite Element Computation of Compressible Flows Involving Moving Boundaries and Interfaces}, YEAR = {1993}, DOI = {10.1016/0045-7825(93)90176-X}, NUMBER = {1--2} } Abstract:
The deformable-spatial-domain/stabilized-space-time (DSD/SST) formulation, introduced by Tezduyar et al. is applied to computation of viscous compressible flows involving moving boundaries and interfaces. The stabilization technique employed is a streamline-upwind/Petrov-Galerkin (SUPG) method, with a modified SUPG stabilization matrix. The stabilized finite element formulation of the governing equations is written over the space-time domain of the problem, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. The frequency of remeshing is minimized to minimize the projection errors involved in remeshing and also to increase the parallelization potential of the computations. The implicit equation systems arising from the space-time finite element discretizations are solved iteratively. It is demonstrated that the combination of the SUPG stabilization and the space-time approach gives the capability of handling complicated compressible flow problems, including those with moving surfaces and shock-boundary layer interactions. © 1993.

[37]

G.J.Le Beau, S.E. Ray, S.K. Aliabadi, and T.E. Tezduyar, “SUPG finite element computation of compressible flows with the entropy and conservation variables formulations”, Computer Methods in Applied Mechanics and Engineering, 104 (1993) 397–422, 10.1016/0045-7825(93)90033-T
@ARTICLE{LeBeau92a, AUTHOR = {G. J.~{Le Beau} and S. E.~Ray and S. K.~Aliabadi and T. E.~Tezduyar}, PAGES = {397--422}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {104}, TITLE = {{SUPG} Finite Element Computation of Compressible Flows with the Entropy and Conservation Variables Formulations}, YEAR = {1993}, DOI = {10.1016/0045-7825(93)90033-T} } Abstract:
SUPG-stabilized finite element formulations of compressible Euler equations based on the conservation and entropy variables are investigated and compared. The formulation based on the conservation variables consists of the formulation introduced by Tezduyar and Hughes plus a shock capturing term. The formulation based on the entropy variables is the same as the one by Hughes, Franca and Mallet, which has a shock capturing term built in. These formulations are tested on several subsonic, transonic and supersonic compressible flow problems. It is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables. Furthermore, the solutions obtained using the two formulations are very close and in some cases almost indistinguishable. Consequently, it can be deduced that the relative merits of these two formulations will continue to remain under debate. © 1993.

[36]

M.A. Behr, L.P. Franca, and T.E. Tezduyar, “Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows”, Computer Methods in Applied Mechanics and Engineering, 104 (1993) 31–48, 10.1016/0045-7825(93)90205-C
@ARTICLE{Behr92a, AUTHOR = {M. A.~Behr and L. P.~Franca and T. E.~Tezduyar}, PAGES = {31--48}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {104}, TITLE = {Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows}, YEAR = {1993}, DOI = {10.1016/0045-7825(93)90205-C}, NUMBER = {1} } Abstract:
Formulated in terms of velocity, pressure and the extra stress tensor, the incompressible Navier-Stokes equations are discretized by stabilized finite element methods. The stabilized methods proposed are analyzed for a linear model and extended to the Navier-Stokes equations. The numerical tests performed confirm the good stability characteristics of the methods. These methods are applicable to various combinations of interpolation functions, including the simplest equal-order linear and bilinear elements. © 1993.

[35]

S. Mittal and T.E. Tezduyar, “Notes on the stabilized space–time finite element formulation of unsteady incompressible flows”, Computer Physics Communications, 73 (1992) 93–112, 10.1016/0010-4655(92)90031-S
@ARTICLE{Mittal92b, AUTHOR = {S.~Mittal and T. E.~Tezduyar}, PAGES = {93--112}, JOURNAL = {Computer Physics Communications}, VOLUME = {73}, TITLE = {Notes on the Stabilized Space--Time Finite Element Formulation of Unsteady Incompressible Flows}, YEAR = {1992}, DOI = {10.1016/0010-4655(92)90031-S} } Abstract:
This paper gives a review of our research efforts on the stabilized space-time finite element formulation of unsteady incompressible flows, including those involving moving boundaries are interfaces. Iterative solution techniques employed to solve the equation systems resulting from the space-time finite element discretization of these flow problems are also reviewed. Results are presented for certain unsteady flow problems, including large-amplitude sloshing and flows past oscillating cylinders. © 1992.

[34]

S. Mittal and T.E. Tezduyar, “A finite element study of incompressible flows past oscillating cylinders and aerofoils”, International Journal for Numerical Methods in Fluids, 15 (1992) 1073–1118, 10.1002/fld.1650150911
@ARTICLE{Mittal91a, AUTHOR = {S.~Mittal and T. E.~Tezduyar}, PAGES = {1073--1118}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {15}, TITLE = {A Finite Element Study of Incompressible Flows Past Oscillating Cylinders and Aerofoils}, YEAR = {1992}, DOI = {10.1002/fld.1650150911} } Abstract:
We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space‐time finite element formulation. The implicit equation systems resulting from the space‐time finite element discretizations are solved using iterative solution techniques. One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex‐shedding pattern of the flow field significantly. This non‐linear fluid‐structure interaction exhibits certain interesting behaviour such as ‘lock‐in’ and ‘hysteresis’, which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented. Copyright © 1992 John Wiley & Sons, Ltd

[33]

O. Pironneau, J. Liou, and T. Tezduyar, “Characteristic-Galerkin and Galerkin/Least-squares Space–Time Formulations for the Advection–Diffusion Equation with Time-dependent Domains”, Computer Methods in Applied Mechanics and Engineering, 100 (1992) 117–141, 10.1016/0045-7825(92)90116-2
@ARTICLE{Pironneau92a, AUTHOR = {O.~Pironneau and J.~Liou and T.~Tezduyar}, PAGES = {117--141}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {100}, TITLE = {Characteristic-{G}alerkin and {G}alerkin/{L}east-squares {S}pace--{T}ime {F}ormulations for the {A}dvection--{D}iffusion {E}quation with {T}ime-dependent {D}omains}, YEAR = {1992}, DOI = {10.1016/0045-7825(92)90116-2} } Abstract:
For the advection-diffusion equation, the characteristic-Galerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are Eulerian-Lagrangian, and therefore can handle time-dependent domains without difficulty. The Galerkin/least-squares space-time formulation, on the other hand, is written over the space-time domain of a problem, and therefore can handle time-dependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advection-diffusion equation. © 1992.

[32]

T.E. Tezduyar, M. Behr, S.K. Aliabadi, S. Mittal, and S.E. Ray, “A new mixed preconditioning method for finite element computations”, Computer Methods in Applied Mechanics and Engineering, 99 (1992) 27–42, 10.1016/0045-7825(92)90121-Y
@ARTICLE{Tezduyar91a, AUTHOR = {T. E.~Tezduyar and M.~Behr and S. K.~Aliabadi and S.~Mittal and S. E.~Ray}, PAGES = {27--42}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {99}, TITLE = {A New Mixed Preconditioning Method for Finite Element Computations}, YEAR = {1992}, DOI = {10.1016/0045-7825(92)90121-Y} } Abstract:
A new mixed clustered element-by-element (CEBE)/cluster companion (CC) preconditioning method for finite element computations is introduced. In the CEBE preconditioning, the elements are merged into clusters of elements, and the preconditioners are defined as series products of cluster level matrices. The CC preconditioning method, which is also introduced in this paper, shares a common philosophy with the multi-grid methods. The CC preconditioners are based on companion meshes associated with different levels of clustering. For each level of clustering, we construct a CEBE preconditioner and an associated CC preconditioner. Because these two preconditioners in a sense complement each other, when they are used in a mixed way, they can be expected to give better performance. In fact, our numerical tests, for two- and three-dimensional problems governed by the Poisson equation, demonstrate that the mixed CEBE/CC preconditioning results in convergence rates which are, in most cases, significantly better than the convergence rates obtained with the best of the CEBE and CC preconditioning methods. © 1992.

[31]

T.E. Tezduyar, “Stabilized finite element formulations for incompressible flow computations”, Advances in Applied Mechanics, 28 (1992) 1–44, 10.1016/S0065-2156(08)70153-4
@ARTICLE{Tezduyar91c, AUTHOR = {T. E.~Tezduyar}, PAGES = {1--44}, JOURNAL = {Advances in Applied Mechanics}, VOLUME = {28}, TITLE = {Stabilized Finite Element Formulations for Incompressible Flow Computations}, YEAR = {1992}, DOI = {10.1016/S0065-2156(08)70153-4} } Abstract:
This chapter discusses stabilized finite element formulations for incompressible flow computations. Finite element computation of incompressible flows involve two main sources of potential numerical instabilities associated with the Galerkin formulation of a problem. The stabilization techniques that are reviewed more extensively than others are the Galerkin/ least-squares (GLS), streamline-upwind/ Petrov–Galerkin (SUPG), and pressure-stabilizing/Petrov–Galerkin (PSPG) formulations. The SUPG stabilization for incompressible flows is achieved by adding to the Galerkin formulation a series of terms, each in the form of an integral over a different element. These integrals involve the product of the residual of the momentum equation and the advective operator acting on the test function. The natural boundary conditions are the conditions on the stress components, and these are the conditions assumed to be imposed at the remaining part of the boundary. The interpolation functions used for velocity and pressure are piecewise bilinear in space and piecewise linear in time. These computations involve no global coefficient matrices, and therefore need substantially less computer memory and time compared to noniterative solution of the fully discrete equations. It is suggested that for two-liquid flows, the solution and variational function spaces for pressure should include the functions that are discontinuous across the interface. © 1992 Academic Press Inc.

[30]

T.E. Tezduyar, M. Behr, S. Mittal, and J. Liou, “A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders”, Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353–371, 10.1016/0045-7825(92)90060-W
@ARTICLE{Tezduyar92b, AUTHOR = {T. E.~Tezduyar and M.~Behr and S.~Mittal and J.~Liou}, PAGES = {353--371}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {94}, TITLE = {A new strategy for finite element computations involving moving boundaries and interfaces -- the deforming-spatial-domain/space--time procedure: {II}.~{C}omputation of free-surface flows, two-liquid flows, and flows with drifting cylinders}, YEAR = {1992}, DOI = {10.1016/0045-7825(92)90060-W}, NUMBER = {3} } Abstract:
New finite element computational strategies for free-surface flows, two-liquid flows, and flows with drifting cylinders are presented. These strategies are based on the deforming spatial-domain/spacetime (DSD/ST) procedure. In the DSD/ST approach, the stabilized variational formulations for these types of flow problem are written over their space-time domains. One of the important features of the approach is that it enables one to circumvent the difficulty involved in remeshing every time step and thus reduces the projection errors introduced by such frequent remeshings. Computations are performed for various test problems mainly for the purpose of demonstrating the computational capability developed for this class of problems. In some of the test cases, such as the liquid drop problem, surface tension is taken into account. For flows involving drifting cylinders, the mesh moving and remeshing schemes proposed are convenient and reduce the frequency of remeshing. © 1992.

[29]

T.E. Tezduyar, M. Behr, and J. Liou, “A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests”, Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339–351, 10.1016/0045-7825(92)90059-S
@ARTICLE{Tezduyar92a, AUTHOR = {T. E.~Tezduyar and M.~Behr and J.~Liou}, PAGES = {339--351}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {94}, TITLE = {A new strategy for finite element computations involving moving boundaries and interfaces -- the deforming-spatial-domain/space--time procedure: {I}.~{T}he concept and the preliminary numerical tests}, YEAR = {1992}, DOI = {10.1016/0045-7825(92)90059-S}, NUMBER = {3} } Abstract:
A new strategy based on the stabilized space-time finite element formulation is proposed for computations involving moving boundaries and interfaces. In the deforming-spatial-domain/space-time (DSD/ST) procedure the variational formulation of a problem is written over its space-time domain, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. Because the space-time mesh is generated over the space-time domain of the problem, within each time step, the boundary (or interface) nodes move with the boundary (or interface). Whether the motion of the boundary is specified or not, the strategy is nearly the same. If the motion of the boundary is unknown, then the boundary nodes move as defined by the other unknowns at the boundary (such as the velocity or the displacement). At the end of each time step a new spatial mesh covers the new spatial domain. For computational feasibility, the finite element interpolation functions are chosen to be discontinuous in time, and the fully discretized equations are solved one space-time slab at a time. © 1992.

[28]

T.E. Tezduyar, S. Mittal, S.E. Ray, and R. Shih, “Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements”, Computer Methods in Applied Mechanics and Engineering, 95 (1992) 221–242, 10.1016/0045-7825(92)90141-6
@ARTICLE{Tezduyar92c, AUTHOR = {T. E.~Tezduyar and S.~Mittal and S. E.~Ray and R.~Shih}, PAGES = {221--242}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {95}, TITLE = {Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements}, YEAR = {1992}, DOI = {10.1016/0045-7825(92)90141-6} } Abstract:
Finite element formulations based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements are presented for computation of steady and unsteady incompressible flows. The stabilization procedure involves a slightly modified Galerkin/least-squares formulation of the steady-state equations. The pressure field is interpolated by continuous functions for both the quadrilateral and triangular elements used. These elements are employed in conjunction with the one-step and multi-step time integration of the Navier-Stokes equations. The three test cases chosen for the performance evaluation of these formulations are the standing vortex problem, the lid-driven cavity flow at Reynolds number 400, and flow past a cylinder at Reynolds number 100. © 1992.

[27]

G.J.Le Beau and T.E. Tezduyar, “Finite element solution of flow problems with mixed-time integration”, Journal of Engineering Mechanics, 117 (1991) 1311–1330, 10.1061/(ASCE)0733-9399(1991)117:6(1311)
@ARTICLE{LeBeau91b, AUTHOR = {G. J.~{Le Beau} and T. E.~Tezduyar}, PAGES = {1311--1330}, JOURNAL = {Journal of Engineering Mechanics}, VOLUME = {117}, TITLE = {Finite Element Solution of Flow Problems with Mixed-Time Integration}, YEAR = {1991}, DOI = {10.1061/(ASCE)0733-9399(1991)117:6(1311)} } Abstract:
A mixed-time integration method that had been developed for the finite element analysis of structural and thermal dynamics has been implemented for the study of both steady and unsteady fluid mechanics problems. The method to be discussed is capable of partitioning the domain into implicit and explicit regions in an attempt to capitalize on the desirable properties of each method, namely the stability and accuracy of the implicit method, and the manageable computational resource demands of an explicit method. In addition, the explicit region is further divided into subregions, each of which may have a different time step that is governed by the local stability criterion of an explicit method. To demonstrate the applicability of these methods to equation systems that govern fluid flow, several examples are presented. These include one- and two-dimensional advection of a cosine hill, as well as two-dimensional steady and unsteady inviscid, compressible flow problems. These examples will be used to show the favorable features of a multi-time integration method, such as a reduction in CPU time, which can be directly attributed to the differing time steps used in the various subregions. © ASCE.

[26]

S. Mittal, H.A. Deans, and T.E. Tezduyar, “Numerical simulation of deep-well wet oxidation reactor using steam”, Journal of Engineering Mechanics, 117 (1991) 798–819, 10.1061/(ASCE)0733-9399(1991)117:4(798)
@ARTICLE{Mittal91c, AUTHOR = {S.~Mittal and H. A.~Deans and T. E.~Tezduyar}, PAGES = {798--819}, JOURNAL = {Journal of Engineering Mechanics}, VOLUME = {117}, TITLE = {Numerical Simulation of Deep-well Wet Oxidation Reactor Using Steam}, YEAR = {1991}, DOI = {10.1061/(ASCE)0733-9399(1991)117:4(798)} } Abstract:
A finite element model is developed for the numerical simulation of the start-up of a deep-well wet oxidation reactor using steam. The model is capable of handling different cases of start-up, using saturated steam of arbitrary quality including hot water. The transient temperature field in the well-earth system is studied. The governing equation for the earth is the conductive heat equation. For the reactor, the analysis involves solving the energy balance equations describing the convective and intertube heat transfer, mass balance equations, and thermodynamic relations for the fluid in the tubes. The equations for the reactor and the earth are coupled by the continuity of the temperature and heat flux at the interface between them. A Galerkin finite element formulation is used for the spatial discretization of the heat equation in the earth; a Petrov-Galerkin finite element formulation is employed for the energy balance equations in the reactor tubes. The resulting set of ordinary differential equations is discretized in time and solved by a predictor-multicorrector algorithm. The model is tested on a typical deep-well reactor to study its start-up dynamics. The results can be used to estimate the startup time and the amount of steam or water required to obtain the necessary initiation temperature for the process. © ASCE.

[25]

M. Behr, J. Liou, R. Shih, and T.E. Tezduyar, “Vorticity-streamfunction formulation of unsteady incompressible flow past a cylinder: sensitivity of the computed flow field to the location of the outflow boundary”, International Journal for Numerical Methods in Fluids, 12 (1991) 323–342, 10.1002/fld.1650120403
@ARTICLE{Behr91b, AUTHOR = {M.~Behr and J.~Liou and R.~Shih and T. E.~Tezduyar}, PAGES = {323--342}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {12}, TITLE = {Vorticity-Streamfunction Formulation of Unsteady Incompressible Flow Past a Cylinder: Sensitivity of the Computed Flow Field to the Location of the Outflow Boundary}, YEAR = {1991}, DOI = {10.1002/fld.1650120403} } Abstract:
The influence of the location of the outflow computational boundary on the unsteady incompressible flow past a circular cylinder at Reynolds number 100 is examined. The vorticity‐streamfunction formulation of the Navier‐Stokes equations is used in all computations. Two types of outflow boundary conditions are subjected to a series of tests in which the domain length is gradually reduced. The traction‐free condition performs well in most cases and allows the outflow boundary to be located as close as 6.5 cylinder diameters from the body. The other boundary condition type is not as forgiving, but has the advantage of being simpler to implement and can still provide reasonably accurate solutions. It is also observed that both condition types can influence the flow field strongly and globally when the boundary is brought closer than 2.5 diameters from the body. In such cases the temporal periodicity of the solution is lost. Copyright © 1991 John Wiley & Sons, Ltd

[24]

T.E. Tezduyar, S. Mittal, and R. Shih, “Time-accurate incompressible flow computations with quadrilateral velocity-pressure elements”, Computer Methods in Applied Mechanics and Engineering, 87 (1991) 363–384, 10.1016/0045-7825(91)90014-W
@ARTICLE{Tezduyar91b, AUTHOR = {T. E.~Tezduyar and S.~Mittal and R.~Shih}, PAGES = {363--384}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {87}, TITLE = {Time-Accurate Incompressible Flow Computations with Quadrilateral Velocity-Pressure Elements}, YEAR = {1991}, DOI = {10.1016/0045-7825(91)90014-W} } Abstract:
Quadrilateral velocity-pressure elements with constant and linear pressure interpolations are examined in the context of time-accurate finite element computation of unsteady incompressible flows. These elements involve streamline-upwind/Petrov-Galerkin stabilization and are implemented in conjunction with the one-step and multi-step temporal integration of the Navier-Stokes equations. The two test cases chosen for the performance evaluation of the formulations are the standing vortex problem and flow past a circular cylinder at Reynolds number 100. © 1991.

[23]

T.E. Tezduyar and R. Shih, “Numerical experiments on downstream boundary of flow past cylinder”, Journal of Engineering Mechanics, 117 (1991) 854–871, 10.1061/(ASCE)0733-9399(1991)117:4(854)
@ARTICLE{Tezduyar91d, AUTHOR = {T. E.~Tezduyar and R.~Shih}, PAGES = {854--871}, JOURNAL = {Journal of Engineering Mechanics}, VOLUME = {117}, TITLE = {Numerical Experiments on Downstream Boundary of Flow Past Cylinder}, YEAR = {1991}, DOI = {10.1061/(ASCE)0733-9399(1991)117:4(854)}, NUMBER = {4} } Abstract:
The influence of the location of the downstream boundary on unsteady incompressible flow solutions is investigated in a series of numerical experiments performed for flow past a circular cylinder at Reynolds number 100. The governing equations are the velocity-pressure formulation of the Navier-Stokes equations, and at the downstream boundary the traction-free condition is imposed. Temporally periodic flow fields obtained by using computational domains with various lengths are compared. It is observed that as far as the near-field solution, the Strouhal number, and the lift and drag coefficients are concerned, the downstream boundary can be placed as close as 14.5 diameters from the center of the cylinder with virtually no difference in the solution. Furthermore, only third-digit variations in the Strouhal number and the lift and drag coefficients and very minor changes in the near-field solution are observed when the downstream boundary is brought as close as 6.5 diameters from the center of the cylinder. Bringing the downstream boundary closer than this seems to result in more significant changes in the solution. In particular, if the distance is 2.6 diameters or closer, the solution becomes symmetric and steady. © ASCE.

[22]

J. Liou, H.A. Deans, and T.E. Tezduyar, “Finite element simulation of deep-well wet oxidation reactor”, Journal of Engineering Mechanics, 116 (1990) 1780–1797, 10.1061/(ASCE)0733-9399(1990)116:8(1780)
@ARTICLE{Liou90c, AUTHOR = {J.~Liou and H. A.~Deans and T. E.~Tezduyar}, PAGES = {1780--1797}, JOURNAL = {Journal of Engineering Mechanics}, VOLUME = {116}, TITLE = {Finite Element Simulation of Deep-well Wet Oxidation Reactor}, YEAR = {1990}, DOI = {10.1061/(ASCE)0733-9399(1990)116:8(1780)} } Abstract:
A finite element model is developed for the numerical simulation of a deep-well wet-oxidation reactor. The temperature distribution in the well-earth system is investigated. The governing equations involved in the analysis are the conductive heat equation for the earth, and an energy balance equation describing convective heat transfer and reaction in the reactor tubes. The two equation sets are coupled by the continuity of the temperature and heat flux at the interface between the earth and the reactor tubes. Proper scaling is carried out for the di-mensionless forms of these equations. A Galerkin finite element formulation is used for the spatial discretization of the heat equation in the earth. A Petrov-Gal-erkin finite element formulation is employed for the convection-reaction equation in the reactor tubes. The resultant set of ordinary differential equations is solved by a predictor/multi-corrector algorithm. A numerical test is performed for a model deep-well reactor. Compared to our previously published work, this formulation is more accurate and consumes less CPU time. It can be used in the design of a deep-well reactor for oxidation of aqueous sludge. It can also be employed to test control strategies for the operating reactor system. © ASCE.

[21]

T.E. Tezduyar and J. Liou, “On the downstream boundary condition for the vorticity-stream function formulation of two-dimensional incompressible flows”, Computer Methods in Applied Mechanics and Engineering, 85 (1991) 207–217, 10.1016/0045-7825(91)90133-Q
@ARTICLE{Tezduyar91e, AUTHOR = {T. E.~Tezduyar and J.~Liou}, PAGES = {207--217}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {85}, TITLE = {On the Downstream Boundary Condition for the Vorticity-Stream Function Formulation of Two-dimensional Incompressible Flows}, YEAR = {1991}, DOI = {10.1016/0045-7825(91)90133-Q } } Abstract:
Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary. © 1991.

[20]

J. Liou and T.E. Tezduyar, “Iterative adaptive implicit-explicit methods for flow problems”, International Journal for Numerical Methods in Fluids, 11 (1990) 867–880, 10.1002/fld.1650110611
@ARTICLE{Liou90b, AUTHOR = {J.~Liou and T. E.~Tezduyar}, PAGES = {867--880}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {11}, TITLE = {Iterative Adaptive Implicit-Explicit Methods for Flow Problems}, YEAR = {1990}, DOI = {10.1002/fld.1650110611} } Abstract:
Iterative versions of the adaptive implicit–explicit method are presented for the finite element computation of flow problems with particular reference to incompressible flows and advection–diffusion problems. The iterative techniques employed are the grouped element‐by‐element and generalized minimum residual methods. Copyright © 1990 John Wiley & Sons, Ltd

[19]

Y.J. Park, H.A. Deans, and T.E. Tezduyar, “Finite element formulation for transport equations in a mixed coordinate system: an application to determine temperature effects on the single-well chemical tracer test”, International Journal for Numerical Methods in Fluids, 11 (1990) 769–790, 10.1002/fld.1650110605
@ARTICLE{Park90a, AUTHOR = {Y. J.~Park and H. A.~Deans and T. E.~Tezduyar}, PAGES = {769--790}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {11}, TITLE = {Finite Element Formulation for Transport Equations in a Mixed Coordinate System: an Application to Determine Temperature Effects on the Single-well Chemical Tracer Test}, YEAR = {1990}, DOI = {10.1002/fld.1650110605} } Abstract:
Heterogeneous equation systems in a pair of coupled co‐ordinate systems are solved by a finite element method. The specific physical application studied is the effect of temperature on single‐well chemical tracer (SWCT) tests to measure residual oil saturation (volume fraction of immobile oil phase) remaining after waterflooding of an oil reservoir. Since temperature effects are caused by injecting cooler surface fluid down a well into a warm reservoir, the vertical temperature profile in the wellbore as well as the temperature distribution in the porous oil‐bearing layer must be considered. The entire system is modelled to account for the different transport mechanisms. However, it is expedient to divide the connected geometrical region into two model domains. The equations for each submodel are expressed in an appropriate set of co‐ordinates. The variational formulation of each model is then discussed. A significant temperature effect on the estimation of residual oil saturation occurs when the radial temperature and concentration wave propagation speeds in the porous formation are about the same. In this case the temperature gradient is located across the chemical tracer bank, causing the chemical reaction rate to vary radially. The temperature effects are demonstrated for two actual field tests in complex reservoirs. Copyright © 1990 John Wiley & Sons, Ltd

[18]

T.E. Tezduyar and J. Liou, “Computation of spatially periodic flows based on the vorticity-stream function formulation”, Computer Methods in Applied Mechanics and Engineering, 83 (1990) 121–142, 10.1016/0045-7825(90)90147-E
@ARTICLE{Tezduyar90d, AUTHOR = {T. E.~Tezduyar and J.~Liou}, PAGES = {121--142}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {83}, TITLE = {Computation of Spatially Periodic Flows Based on the Vorticity-Stream Function Formulation}, YEAR = {1990}, DOI = {10.1016/0045-7825(90)90147-E} } Abstract:
Finite element solution strategies are presented for the two-dimensional, spatially periodic, viscous and inviscid, incompressible flows governed by the verticity-stream function formulation. These strategies are successfully tested on various uniperiodic and biperiodic viscous flow problems involving arrays of cylinders with Reynolds number 0 and 100. It is shown that in all cases for Reynolds number 100 the solution becomes unsteady and ceases to satisfy the symmetry conditions along the horizontal centerlines of the cylinders. © 1990.

[17]

T.E. Tezduyar, J. Liou, and D.K. Ganjoo, “Incompressible flow computations based on the vorticity-stream function and velocity-pressure formulations”, Computers & Structures, 35 (1990) 445–472, 10.1016/0045-7949(90)90069-E
@ARTICLE{Tezduyar90b, AUTHOR = {T. E.~Tezduyar and J.~Liou and D. K.~Ganjoo}, PAGES = {445--472}, JOURNAL = {Computers \& Structures}, VOLUME = {35}, TITLE = {Incompressible FLow Computations Based on the Vorticity-Stream Function and Velocity-Pressure Formulations}, YEAR = {1990}, DOI = {10.1016/0045-7949(90)90069-E}, NUMBER = {4} } Abstract:
Finite element procedures and computations based on the velocity-pressure and vorticitystream function formulations of incompressible flows are presented. Two new multi-step velocity-pressure formulations are proposed and are compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Benchmark quality computations are performed for the cylinder problem. The numerical results indicate that the vorticity-stream function formulation and one of the two new multi-step formulations involve much less numerical dissipation than the one-step formulation. © 1990.

[16]

T.E. Tezduyar and J. Liou, “Adaptive implicit-explicit finite element algorithms for fluid mechanics problems”, Computer Methods in Applied Mechanics and Engineering, 78 (1990) 165–179, 10.1016/0045-7825(90)90099-8
@ARTICLE{Tezduyar90c, AUTHOR = {T. E.~Tezduyar and J.~Liou}, PAGES = {165--179}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {78}, TITLE = {Adaptive Implicit-Explicit Finite Element Algorithms for Fluid Mechanics Problems}, YEAR = {1990}, DOI = {10.1016/0045-7825(90)90099-8} } Abstract:
The adaptive implicit-explicit (AIE) approach is presented for the finite element solution of various problems in computational fluid mechanics. In the AIE approach the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that with this approach substantial savings in the CPU time and memory can be achieved. © 1990.

[15]

T.E. Tezduyar, J. Liou, D.K. Ganjoo, and M. Behr, “Solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows”, International Journal for Numerical Methods in Fluids, 11 (1990) 515–539, 10.1002/fld.1650110505
@ARTICLE{Tezduyar90a, AUTHOR = {T. E.~Tezduyar and J.~Liou and D. K.~Ganjoo and M.~Behr}, PAGES = {515--539}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {11}, TITLE = {Solution Techniques for the Vorticity-Streamfunction Formulation of Two-dimensional unsteady Incompressible Flows}, YEAR = {1990}, DOI = {10.1002/fld.1650110505} } Abstract:
A review of our solution techniques for the vorticity–streamfunction formulation of two‐dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov–Galerkin method is used. The adaptive implicit–explicit and grouped element‐by‐element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable and efficient. Copyright © 1990 John Wiley & Sons, Ltd

[14]

T.E. Tezduyar, “Finite element formulation for the vorticity-stream function form of the incompressible Euler equations on multiply-connected domains”, Computer Methods in Applied Mechanics and Engineering, 73 (1989) 331–339, 10.1016/0045-7825(89)90072-8
@ARTICLE{Tezduyar89b, AUTHOR = {T. E.~Tezduyar}, PAGES = {331--339}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {73}, TITLE = {Finite Element Formulation for the Vorticity-Stream Function Form of the Incompressible {E}uler Equations on Multiply-connected Domains}, YEAR = {1989}, DOI = {10.1016/0045-7825(89)90072-8} } Abstract:
A proper finite element formulation is derived for the vorticity-stream function form of the incompressible Euler equations on two-dimensional multiply-connected domains. The formulation includes the variational equation needed for determining the value of the stream function at the internal boundaries. © 1989.

[13]

T.E. Tezduyar and J. Liou, “Grouped element-by-element iteration schemes for incompressible flow computations”, Computer Physics Communications, 53 (1989) 441–453, 10.1016/0010-4655(89)90177-X
@ARTICLE{Tezduyar89a, AUTHOR = {T. E.~Tezduyar and J.~Liou}, PAGES = {441--453}, JOURNAL = {Computer Physics Communications}, VOLUME = {53}, TITLE = {Grouped Element-by-Element Iteration Schemes for Incompressible Flow Computations}, YEAR = {1989}, DOI = {10.1016/0010-4655(89)90177-X} } Abstract:
Grouped element-by-element (GEBE) iteration schemes for incompressible flows are presented in the context of vorticity- stream function formulation. The GEBE procedure is a variation of the EBE procedure and is based on arrangement of the elements into groups with no inter-element coupling within each group. With the GEBE approach, vectorization and parallel implementation of the EBE method becomes more clear. The savings in storage and CPU time are demonstrated with two unsteady flow problems. © 1989.

[12]

D.K. Ganjoo, T.E. Tezduyar, and W.D. Goodrich, “A new formulation for numerical solution of electrophoresis separation processes”, Computer Methods in Applied Mechanics and Engineering, 75 (1989) 515–530, 10.1016/0045-7825(89)90045-5
@ARTICLE{Ganjoo89a, AUTHOR = {D. K.~Ganjoo and T. E.~Tezduyar and W. D.~Goodrich}, PAGES = {515--530}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {75}, TITLE = {A New Formulation for Numerical Solution of Electrophoresis Separation Processes}, YEAR = {1989}, DOI = {10.1016/0045-7825(89)90045-5} } Abstract:
A new numerical simulation model for electrophoresis separation phenomena is presented. The proposed model employs a Petrov-Galerkin scheme to solve for the concentrations, the electric potential and its gradient via a mixed finite element formulation. This formulation does not involve any restrictions on the electric current density or the finite element mesh. The scheme is stable, accurate, and can be applied to intricate geometries in higher space dimensions without loss of generality. Moreover this formulation avoids the usage of higher order elements which can be expensive. Example simulations are performed in one and two space dimensions. The one-dimensional results closely agree with those from past publications. The success of the simulations in two dimensions indicates the potential of the scheme to address design strategies in practical separation techniques. © 1989.

[11]

T.E. Tezduyar, R. Glowinski, and J. Liou, “Petrov-Galerkin methods on multiply-connected domains for the vorticity-stream function formulation of the incompressible Navier-Stokes equations”, International Journal for Numerical Methods in Fluids, 8 (1988) 1269–1290, 10.1002/fld.1650081012
@ARTICLE{Tezduyar88a, AUTHOR = {T. E.~Tezduyar and R.~Glowinski and J.~Liou}, PAGES = {1269--1290}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {8}, TITLE = {{P}etrov-{G}alerkin Methods on Multiply-connected Domains for the Vorticity-Stream Function Formulation of the Incompressible {N}avier-{S}tokes Equations}, YEAR = {1988}, DOI = {10.1002/fld.1650081012} } Abstract:
In this paper we present streamline‐upwind/Petrov‐Galerkin finite element procedures for two‐dimensional fluid dynamics computations based on the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no‐slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block‐iteration methods, have successfully been applied to various problems involving simply and multiply connected domains. Copyright © 1988 John Wiley & Sons, Ltd

[10]

D.K. Ganjoo and T.E. Tezduyar, “Petrov-Galerkin formulations for electrochemical processes”, Computer Methods in Applied Mechanics and Engineering, 65 (1987) 61–83, 10.1016/0045-7825(87)90183-6
@ARTICLE{Ganjoo87a, AUTHOR = {D. K.~Ganjoo and T. E.~Tezduyar}, PAGES = {61--83}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {65}, TITLE = {{P}etrov-{G}alerkin Formulations for Electrochemical Processes}, YEAR = {1987}, DOI = {10.1016/0045-7825(87)90183-6} } Abstract:
A numerical simulation capability has been developed for electrochemical processes, in particular for electrophoresis separation techniques. The numerical method employed is based on the streamline upwind/Petrov-Galerkin formulations which have desirable stability and accuracy properties for the convection-diffusion-reaction type equations that govern these problems. Simulations are performed for various electrophoresis separation types in one and two dimensions. The results obtained are very satisfactory and show the potential of the numerical method to be a useful tool in understanding the physics involved and in helping the design of reliable and efficient separation techniques. © 1987.

[ 9]

T.E. Tezduyar, Y.J. Park, and H.A. Deans, “Finite element procedures for time-dependent convection-diffusion-reaction systems”, International Journal for Numerical Methods in Fluids, 7 (1987) 1013–1033, 10.1002/fld.1650071003
@ARTICLE{Tezduyar87a, AUTHOR = {T. E.~Tezduyar and Y. J.~Park and H. A.~Deans}, PAGES = {1013--1033}, JOURNAL = {International Journal for Numerical Methods in Fluids}, VOLUME = {7}, TITLE = {Finite Element Procedures for Time-dependent Convection-Diffusion-Reaction Systems}, YEAR = {1987}, DOI = {10.1002/fld.1650071003} } Abstract:
New finite element procedures based on the streamline‐upwind/Petrov‐Galerkin formulations are developed for time‐dependent convection‐diffusion‐reaction equations. These procedures minimize spurious oscillations for convection‐dominated and reaction‐dominated problems. The results obtained for representative numerical examples are accurate with minimal oscillations. As a special application problem, the single‐well chemical tracer test (a procedure for measuring oil remaining in a depleted field) is simulated numerically. The results show the importance of temperature effects on the interpreted value of residual oil saturation from such tests. Copyright © 1987 John Wiley & Sons, Ltd

[ 8]

T.E. Tezduyar and Y.J. Park, “Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations”, Computer Methods in Applied Mechanics and Engineering, 59 (1986) 307–325, 10.1016/0045-7825(86)90003-4
@ARTICLE{Tezduyar86a, AUTHOR = {T. E.~Tezduyar and Y. J.~Park}, PAGES = {307--325}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {59}, TITLE = {Discontinuity Capturing Finite Element Formulations for Nonlinear Convection-Diffusion-Reaction Equations}, YEAR = {1986}, DOI = {10.1016/0045-7825(86)90003-4} } Abstract:
Formulations which complement the streamline-upwind/Petrov-Galerkin procedure are presented. These formulations minimize the oscillations about sharp internal and boundary layers in convection-dominated and reaction-dominated flows. The proposed methods are tested on various single- and multi-component transport problems. © 1986.

[ 7]

T.E. Tezduyar, L.T. Wheeler, and L. Graux, “Finite deformation of a circular elastic membrane containing a concentric rigid inclusion”, International Journal of Nonlinear Mechanics, 22 (1987) 61–72, 10.1016/0020-7462(87)90049-7
@ARTICLE{Tezduyar87b, AUTHOR = {T. E.~Tezduyar and L. T.~Wheeler and L.~Graux}, PAGES = {61--72}, JOURNAL = {International Journal of Nonlinear Mechanics}, VOLUME = {22}, TITLE = {Finite Deformation of a Circular Elastic Membrane Containing a Concentric Rigid Inclusion}, YEAR = {1987}, DOI = {10.1016/0020-7462(87)90049-7} } Abstract:
Results are reported for the axisymmetric response of an initially flat annular membrane to transverse deflections of a rigid inclusion centered within the membrane. The membrane material is assumed to behave elastically in accordance with the Mooney-Rivlin constitutive law. The response shows a dramatic change in features with variations in one of the two Mooney-Rivlin parameters. Corresponding to negative values of this parameter, the membrane wrinkles for sufficiently high loads, whereas for positive values and large enough loads, it assumes an hourglass profile without wrinkling. For the case when this parameter vanishes, in which case it is of the neo-Hookean type, the load may be increased indefinitely without causing the membrane to wrinkle or go into an hourglass profile. The non-linear system of first-order differential equations governing the problem is solved by a predictor/multi-corrector integration method. © 1987.

[ 6]

T.E. Tezduyar and D.K. Ganjoo, “Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: applications to transient convection-diffusion problems”, Computer Methods in Applied Mechanics and Engineering, 59 (1986) 49–71, 10.1016/0045-7825(86)90023-X
@ARTICLE{Tezduyar86b, AUTHOR = {T. E.~Tezduyar and D. K.~Ganjoo}, PAGES = {49--71}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {59}, TITLE = {Petrov-{G}alerkin Formulations with Weighting Functions Dependent upon Spatial and Temporal Discretization: Applications to Transient Convection-Diffusion Problems}, YEAR = {1986}, DOI = {10.1016/0045-7825(86)90023-X} } Abstract:
A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which take into account temporal as well as spatial discretization, provide improved solutions. In view of the generality of the differential equation being solved, these schemes can be implemented for any physical problem which is governed by the transient convection-diffusion equation. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and Navier-Stokes equations. © 1986.

[ 5]

L.T. Wheeler, T.E. Tezduyar, and B.H. Eldiwany, “Profiles of minimum stress concentration for antiplane deformation of an elastic solid”, Journal of Elasticity, 15 (1985) 271–282, 10.1007/BF00041425
@ARTICLE{Wheeler85a, AUTHOR = {L. T.~Wheeler and T. E.~Tezduyar and B. H.~Eldiwany}, PAGES = {271--282}, JOURNAL = {Journal of Elasticity}, VOLUME = {15}, TITLE = {Profiles of Minimum Stress Concentration for Antiplane Deformation of an Elastic Solid}, YEAR = {1985}, DOI = {10.1007/BF00041425} }

[ 4]

T.J.R. Hughes and T.E. Tezduyar, “Analysis of some fully-discrete algorithms for the one-dimensional heat equation”, International Journal of Numerical Methods in Engineering, 21 (1985) 163–168, 10.1002/nme.1620210113
@ARTICLE{Hughes85a, AUTHOR = {T. J. R.~Hughes and T. E.~Tezduyar}, PAGES = {163--168}, JOURNAL = {International Journal of Numerical Methods in Engineering}, VOLUME = {21}, TITLE = {Analysis of Some Fully-discrete Algorithms for the One-dimensional Heat Equation}, YEAR = {1985}, DOI = {10.1002/nme.1620210113} } Abstract:
A fully discrete stability and accuracy analysis of some algorithms for the one‐dimensional heat equation is presented. Results illustrate that 2‐pass explicit schemes which simultaneously employ lumped and coupled capacity matrices are capable of improved performance over the standard 1‐pass explicit scheme. Copyright © 1985 John Wiley & Sons, Ltd

[ 3]

T.J.R. Hughes and T.E. Tezduyar, “Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations”, Computer Methods in Applied Mechanics and Engineering, 45 (1984) 217–284, 10.1016/0045-7825(84)90157-9
@ARTICLE{Hughes84a, AUTHOR = {T. J. R.~Hughes and T. E.~Tezduyar}, PAGES = {217--284}, JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, VOLUME = {45}, TITLE = {Finite Element Methods for First-order Hyperbolic Systems with Particular Emphasis on the Compressible {E}uler Equations}, YEAR = {1984}, DOI = {10.1016/0045-7825(84)90157-9} } Abstract:
A Petrov-Galerkin finite element formulation is presented for first-order hyperbolic systems of conservation laws with particular emphasis on the compressible Euler equations. Applications of the methodology are made to one- and two-dimensional steady and unsteady flows with shocks. Results obtained suggest the potential of the type of methods developed. © 1984.

[ 2]

T.J.R. Hughes and T.E. Tezduyar, “Stability and accuracy analysis of some fully-discrete algorithms for the one-dimensional second-order wave equation”, Computers & Structures, 19 (1984) 665–668, 10.1016/0045-7949(84)90113-5
@ARTICLE{Hughes84b, AUTHOR = {T. J. R.~Hughes and T. E.~Tezduyar}, PAGES = {665--668}, JOURNAL = {Computers \& Structures}, VOLUME = {19}, TITLE = {Stability and Accuracy Analysis of Some Fully-discrete Algorithms for the One-dimensional Second-order Wave Equation}, YEAR = {1984}, DOI = {10.1016/0045-7949(84)90113-5} } Abstract:
Stability and accuracy properties of some fully discrete algorithms for the one-dimensional wave equation are presented. Emphasis is placed on so-called 2-pass explicit schemes in which lumped and coupled mass matrices are employed. © 1984.

[ 1]

T.J.R. Hughes and T.E. Tezduyar, “Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element”, Journal of Applied Mechanics, 48 (1981) 587–596 also in New Concepts in Finite Element Analysis, AMD-Vol. 44, ASME, New York (1981) 81-106, 10.1115/1.3157679
@ARTICLE{Hughes81b, AUTHOR = {T. J. R.~Hughes and T. E.~Tezduyar}, PAGES = {587--596}, JOURNAL = {Journal of Applied Mechanics}, VOLUME = {48}, TITLE = {Finite Elements Based Upon {M}indlin Plate Theory with Particular Reference to the Four-node Bilinear Isoparametric Element}, YEAR = {1981}, DOI = {10.1115/1.3157679}, NOTE = {also in New Concepts in Finite Element Analysis, AMD-Vol. 44, ASME, New York (1981) 81-106} } Abstract:
Concepts useful for the development of Mindlin plate elements are explored. Interpolato-ry schemes and nodal patterns which are ideal according to the proposed criteria are found to be somewhat more complicated than desirable for practical applications. However, these ideas are found to be useful as starting points in the development of simpler elements. This is illustrated by the derivation of a new four-node bilinear quadrilateral which achieves good accuracy without ostensible defect. © 1981 by ASME.

Other Journal Articles

[26]

K. Takizawa, Y. Bazilevs, T.E. Tezduyar, M.-C. Hsu, and T. Terahara, “Computational cardiovascular medicine with isogeometric analysis”, Journal of Advanced Engineering and Computation, 6 (2022) 167–199, 10.55579/jaec.202263.381
@ARTICLE{Takizawa22b, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar and Ming-Chen Hsu and T.~Terahara}, PAGES = {167--199}, JOURNAL = {Journal of Advanced Engineering and Computation}, VOLUME = {6}, TITLE = {Computational Cardiovascular Medicine With Isogeometric Analysis}, YEAR = {2022}, DOI = {10.55579/jaec.202263.381} }

[25]

K. Takizawa, Y. Bazilevs, and T.E. Tezduyar, “Mesh moving methods in flow computations with the space–time and arbitrary Lagrangian–Eulerian methods”, Journal of Advanced Engineering and Computation, 6 (2022) 85–112, 10.55579/jaec.202262.377
@ARTICLE{Takizawa22a, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar}, PAGES = {85--112}, JOURNAL = {Journal of Advanced Engineering and Computation}, VOLUME = {6}, TITLE = {Mesh Moving Methods in Flow Computations With the Space--Time and Arbitrary {L}agrangian--{E}ulerian Methods}, YEAR = {2022}, DOI = {10.55579/jaec.202262.377} }

[24]

K. Takizawa, Y. Bazilevs, T.E. Tezduyar, and A. Korobenko, “Computational flow analysis in aerospace, energy and transportation technologies with the variational multiscale methods”, Journal of Advanced Engineering and Computation, 4 (2020) 83–117, 10.25073/jaec.202042.279
@ARTICLE{Takizawa20a, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar and A.~Korobenko}, PAGES = {83--117}, JOURNAL = {Journal of Advanced Engineering and Computation}, VOLUME = {4}, TITLE = {Computational Flow Analysis in Aerospace, Energy and Transportation Technologies with the Variational Multiscale Methods}, YEAR = {2020}, DOI = {10.25073/jaec.202042.279} }

[23]

Y. Bazilevs, K. Takizawa, T.E. Tezduyar, M.-C. Hsu, Y. Otoguro, H. Mochizuki, and M.C.H. Wu, “Wind turbine and turbomachinery computational analysis with the ALE and space–time variational multiscale methods and isogeometric discretization”, Journal of Advanced Engineering and Computation, 4 (2020) 1–32, 10.25073/jaec.202041.278
@ARTICLE{Bazilevs20a, AUTHOR = {Y.~Bazilevs and K.~Takizawa and T. E.~Tezduyar and Ming-Chen Hsu and Y.~Otoguro and H.~Mochizuki and M. C. H.~Wu}, PAGES = {1--32}, JOURNAL = {Journal of Advanced Engineering and Computation}, VOLUME = {4}, TITLE = {Wind Turbine and Turbomachinery Computational Analysis with the {ALE} and Space--Time Variational Multiscale Methods and Isogeometric Discretization}, YEAR = {2020}, DOI = {10.25073/jaec.202041.278} }

[22]

K. Takizawa, Y. Bazilevs, T.E. Tezduyar, and M.-C. Hsu, “Computational cardiovascular flow analysis with the variational multiscale methods”, Journal of Advanced Engineering and Computation, 3 (2019) 366–405, 10.25073/jaec.201932.245
@ARTICLE{Takizawa19a, AUTHOR = {K.~Takizawa and Y.~Bazilevs and T. E.~Tezduyar and Ming-Chen Hsu}, PAGES = {366--405}, JOURNAL = {Journal of Advanced Engineering and Computation}, VOLUME = {3}, TITLE = {Computational Cardiovascular Flow Analysis with the Variational Multiscale Methods}, YEAR = {2019}, DOI = {10.25073/jaec.201932.245} }

[21]

K. Takizawa, T.E. Tezduyar, and T. Kanai, “Spacecraft-parachute computational analysis and compressible-flow extensions”, Japan Aeronautical and Space Sciences Magazine, 65 (2017) 280–283 in Japanese, 10.14822/kjsass.65.9_280
@ARTICLE{Takizawa17d, AUTHOR = {K.~Takizawa and T. E.~Tezduyar and T.~Kanai}, PAGES = {280--283}, JOURNAL = {Japan Aeronautical and Space Sciences Magazine}, VOLUME = {65}, TITLE = {Spacecraft-Parachute Computational Analysis and Compressible-Flow Extensions}, YEAR = {2017}, DOI = {10.14822/kjsass.65.9_280}, NUMBER = {9}, NOTE = {in Japanese} }

[20]

K. Takizawa and T.E. Tezduyar, “Main aspects of the space–time computational FSI techniques and examples of challenging problems solved”, Mechanical Engineering Reviews, 1 (2014) CM0005 inaugural issue, 10.1299/mer.2014cm0005
@ARTICLE{Takizawa13f, AUTHOR = {K.~Takizawa and T. E.~Tezduyar}, PAGES = {CM0005}, JOURNAL = {Mechanical Engineering Reviews}, VOLUME = {1}, TITLE = {Main Aspects of the Space--Time Computational {FSI} Techniques and Examples of Challenging Problems Solved}, YEAR = {2014}, DOI = {10.1299/mer.2014cm0005}, PUBLISHER = {Japan Society of Mechanical Engineers}, NOTE = {{\bf inaugural issue}} }

[19]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Coupling 3D fluid–structure interaction modeling of cerebral aneurysm with 0D arterial network model as boundary conditions”, Transactions of the Japan Society for Simulation Technology, 1 (2009) 81–90, 10.11308/tjsst.1.81
@ARTICLE{Torii09b, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {81--90}, JOURNAL = {Transactions of the Japan Society for Simulation Technology}, VOLUME = {1}, TITLE = {Coupling {3D} Fluid--Structure Interaction Modeling of Cerebral Aneurysm with {0D} Arterial Network Model as Boundary Conditions}, YEAR = {2009}, DOI = {10.11308/tjsst.1.81} }

[18]

R. Torii, M. Oshima, T. Kobayashi, K. Takagi, and T.E. Tezduyar, “Influence of wall elasticity on image-based blood flow simulations”, Transactions of the Japan Society of Mechanical Engineers Series A, 70 (2004) 1224–1231 in Japanese, 10.1299/kikaia.70.1224
@ARTICLE{Torii04b, AUTHOR = {R.~Torii and M.~Oshima and T.~Kobayashi and K.~Takagi and T. E.~Tezduyar}, PAGES = {1224--1231}, JOURNAL = {Transactions of the Japan Society of Mechanical Engineers Series A}, VOLUME = {70}, TITLE = {Influence of Wall Elasticity on Image-Based Blood Flow Simulations}, YEAR = {2004}, DOI = {10.1299/kikaia.70.1224}, NOTE = {in Japanese} } Abstract:
Recently, it is reported that risk of rupture of aneurysms is further less than risk of surgical complications. Therefore, to avoid unnecessary surgical operations, prediction of rupture of aneurysms is necessary. Because wall shear stress is known to play an important role for a vascular disease, the authors have investigated the relationship between wall shear stress and cerebral aneurysms. In this paper, numerical fluid-structure interaction analyses are performed to investigate influences of wall deformation on hemodynamic factors. The results show several patterns of arterial wall deformations and their influences on blood flow behavior and hemodynamic factors.

[17]

L. Catabriga, A.L.G.A. Coutinho, and T.E. Tezduyar, “Compressible flow SUPG stabilization parameters computed from element-edge matrices”, Computational Fluid Dynamics Journal, 13 (2004) 450–459
@ARTICLE{Catabriga04a, AUTHOR = {L.~Catabriga and A. L. G. A.~Coutinho and T. E.~Tezduyar}, PAGES = {450--459}, JOURNAL = {Computational Fluid Dynamics Journal}, VOLUME = {13}, TITLE = {Compressible Flow {SUPG} Stabilization Parameters Computed from Element-Edge Matrices}, YEAR = {2004} }

[16]

T.E. Tezduyar, “Stabilized finite element methods for flows with moving boundaries and interfaces”, HERMIS: The International Journal of Computer Mathematics and its Applications, 4 (2003) 63–88
@ARTICLE{Tezduyar04a, AUTHOR = {T. E.~Tezduyar}, PAGES = {63--88}, JOURNAL = {{HERMIS:} The International Journal of Computer Mathematics and its Applications}, VOLUME = {4}, TITLE = {Stabilized Finite Element Methods for Flows with Moving Boundaries and Interfaces}, YEAR = {2003} }

[15]

K. Stein, T. Tezduyar, R. Benney, M. Accorsi, and H. Johari, “Computational modeling of parachute fluid-structure interactions”, Computational Fluid Dynamics Journal, 12 (2003) 516–526
@ARTICLE{Stein02a, AUTHOR = {K.~Stein and T.~Tezduyar and R.~Benney and M.~Accorsi and H.~Johari}, PAGES = {516--526}, JOURNAL = {Computational Fluid Dynamics Journal}, VOLUME = {12}, TITLE = {Computational Modeling of Parachute Fluid-Structure Interactions}, YEAR = {2003} }

[14]

T.E. Tezduyar, “Calculation of the stabilization parameters in finite element formulations of flow problems”, Applications of Computational Mechanics in Structures and Fluids (2005) 1–19
@INCOLLECTION{Tezduyar03b, AUTHOR = {T. E.~Tezduyar}, PAGES = {1--19}, TITLE = {Calculation of the Stabilization Parameters in Finite Element Formulations of Flow Problems}, YEAR = {2005}, PUBLISHER = {CIMNE}, BOOKTITLE = {Applications of Computational Mechanics in Structures and Fluids}, ADDRESS = {Barcelona, Spain}, EDITOR = {S. R.~Idelsohn and V.~Sonzogni}, ISBN = {84-95999-85-4} }

[13]

T. Tezduyar and S. Sathe, “Stabilization parameters in SUPG and PSPG formulations”, Journal of Computational and Applied Mechanics, 4 (2003) 71–88
@ARTICLE{Tezduyar02g, AUTHOR = {T.~Tezduyar and S.~Sathe}, PAGES = {71--88}, JOURNAL = {Journal of Computational and Applied Mechanics}, VOLUME = {4}, TITLE = {Stabilization Parameters in {SUPG} and {PSPG} Formulations}, YEAR = {2003} }

[12]

A.M.K. Anderson and T.E. Tezduyar, “A K-PhD education program in flow simulation and modeling”, Computational Fluid Dynamics Journal, 9 (2000) 242–251
@ARTICLE{Anderson00a, AUTHOR = {A. M. K.~Anderson and T. E.~Tezduyar}, PAGES = {242--251}, JOURNAL = {Computational Fluid Dynamics Journal}, VOLUME = {9}, TITLE = {A {K-PhD} Education Program in Flow Simulation and Modeling}, YEAR = {2000} }

[11]

W.B. Sturek, T.E. Tezduyar, and P. Muzio, “Army High Performance Computing Research Center: a unique resource for defense basic research and education”, Army RD& A, September–October (1999) 44–45
@ARTICLE{Sturek99a, AUTHOR = {W. B.~Sturek and T. E.~Tezduyar and P.~Muzio}, PAGES = {44--45}, JOURNAL = {Army RD\& A}, VOLUME = {September--October}, TITLE = {{A}rmy {H}igh {P}erformance {C}omputing {R}esearch {C}enter: A Unique Resource for Defense Basic Research and Education}, YEAR = {1999} }

[10]

Y. Osawa and T. Tezduyar, “3D simulation and visualization of unsteady wake flow behind a cylinder”, Journal of Visualization, 2 (1999) 127–134, 10.1007/BF03181515
@ARTICLE{Osawa99b, AUTHOR = {Y.~Osawa and T.~Tezduyar}, PAGES = {127--134}, JOURNAL = {Journal of Visualization}, VOLUME = {2}, TITLE = {{3D} Simulation and Visualization of Unsteady Wake Flow Behind a Cylinder}, YEAR = {1999}, DOI = {10.1007/BF03181515} } Abstract:
In this paper we focus on 3D simulation of unsteady wake flow behind a circular cylinder. We show that in addition to accurate formulations and sufficiently-refined meshes, efficient computing methods are essential components of an effective simulation strategy. We use the Multi-Domain Method (MDM) we developed recently in computation of two cases. At Reynolds number 300, we demonstrate how the MDM enables us to use highly-refined meshes to capture wake patterns which we otherwise cannot fully represent. At Reynolds number 140, we show that with the MDM we can extend our computations sufficiently downstream, and with sufficient accuracy, to successfully capture the second phase of the Karman vortex street, which has been observed in laboratory experiments, and which has double the spacing between the vortices compared to the first phase.

[ 9]

Y. Osawa and T. Tezduyar, “A multi-domain method for 3D computation of wake flow behind a circular cylinder”, Computational Fluid Dynamics Journal, 8 (1999) 296–308
@ARTICLE{Osawa99a, AUTHOR = {Y.~Osawa and T.~Tezduyar}, PAGES = {296--308}, JOURNAL = {Computational Fluid Dynamics Journal}, VOLUME = {8}, TITLE = {A Multi-Domain Method for {3D} Computation of Wake Flow Behind a Circular Cylinder}, YEAR = {1999} }

[ 8]

V. Kalro and T. Tezduyar, “Parallel iterative computational methods for 3D finite element flow simulations”, Computer Assisted Mechanics and Engineering Sciences, 5 (1998) 173–183
@ARTICLE{Kalro97a, AUTHOR = {V.~Kalro and T.~Tezduyar}, PAGES = {173--183}, JOURNAL = {Computer Assisted Mechanics and Engineering Sciences}, VOLUME = {5}, TITLE = {Parallel Iterative Computational Methods for {3D} Finite Element Flow Simulations}, YEAR = {1998} }

[ 7]

J. Chandra and T. Tezduyar, “High performance computing: an Army initiative”, Army RD& A, May–June (1995) 28–31
@ARTICLE{Chandra95a, AUTHOR = {J.~Chandra and T.~Tezduyar}, PAGES = {28--31}, JOURNAL = {Army RD\& A}, VOLUME = {May--June}, TITLE = {High Performance Computing: an {A}rmy Initiative}, YEAR = {1995} }

[ 6]

T.E. Tezduyar, “The Army High Performance Computing Research Center”, IEEE Computational Science and Engineering, 1 (1994) 6–8, 10.1109/99.326670
@ARTICLE{Tezduyar94c, AUTHOR = {T. E.~Tezduyar}, PAGES = {6--8}, JOURNAL = {IEEE Computational Science and Engineering}, VOLUME = {1}, TITLE = {The {A}rmy {H}igh {P}erformance {C}omputing {R}esearch {C}enter}, YEAR = {1994}, DOI = {10.1109/99.326670}, ISSUE = {2} }

[ 5]

A.A. Johnson, T.E. Tezduyar, and J. Liou, “Numerical simulation of flows past periodic arrays of cylinders”, Computational Mechanics, 11 (1993) 371–383, 10.1007/BF00350094
@ARTICLE{Johnson93a, AUTHOR = {A. A.~Johnson and T. E.~Tezduyar and J.~Liou}, PAGES = {371--383}, JOURNAL = {Computational Mechanics}, VOLUME = {11}, TITLE = {Numerical Simulation of Flows Past Periodic Arrays of Cylinders}, YEAR = {1993}, DOI = {10.1007/BF00350094} } Abstract:
We present a detailed numerical investigation of three unsteady incompressible flow problems involving periodic arrays of staggered cylinders. The first problem is a uniperiodic flow with two cylinders in each cell of periodicity. The second problem is a biperiodic flow with two cylinders in each cell, and the last problem is a uniperiodic flow with ten cylinders. Both uniperiodic flows are periodic in the direction perpendicular to the main flow direction. In all three cases, the Reynolds number based on the cylinder diameter is 100, and initially the flow field has local symmetries with respect to the axes of the cylinders parallel to the main flow direction. Later on, these symmetries break, vortex shedding is initiated, and gradually the scale of the shedding increases until a temporally periodic flow field is reached. We furnish extensive flow data, including the vorticity and stream function fields at various instants during the temporal evolution of the flow field, time histories of the drag and lift coefficients, Strouhal number, initial and mean drag coefficients, amplitude of the drag and lift coefficient oscillations, and the phase relationships between the drag and lift oscillations associated with each cylinder. Our data confirms that, at this Reynolds number, there are no stable steady-state solutions with local symmetries. Of course, one can obtain such unphysical solutions by assuming symmetry conditions along the axes of the cylinders parallel to the main flow direction and taking half of the computational domain needed normally. In such cases, the "steady-state" flow fields obtained would be identical to the flow fields observed at the initial stages of our computations. However, we show that such flow fields do not represent the temporally periodic flow fields even in a time-averaged sense, because, in all three cases, the initial drag coefficients are different from the mean drag coefficients. Therefore, we conclude that stability studies involving periodic arrays of cylinders should be carried out, as it is done in this work, with the true implementation of the spatial periodicity. © 1993 Springer-Verlag.

[ 4]

S.K. Aliabadi, S.E. Ray, and T.E. Tezduyar, “SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations”, Computational Mechanics, 11 (1993) 300–312, 10.1007/BF00350089
@ARTICLE{Aliabadi93a, AUTHOR = {S. K.~Aliabadi and S. E.~Ray and T. E.~Tezduyar}, PAGES = {300--312}, JOURNAL = {Computational Mechanics}, VOLUME = {11}, TITLE = {{SUPG} Finite Element Computation of Viscous Compressible Flows Based on the Conservation and Entropy Variables Formulations}, YEAR = {1993}, DOI = {10.1007/BF00350089} } Abstract:
In this article, we present our investigation and comparison of the SUPG-stabilized finite element formulations for computation of viscous compressible flows based on the conservation and entropy variables. This article is a sequel to the one on inviscid compressible flows by Le Beau et al. (1992). For the conservation variables formulation, we use the SUPG stabilization technique introduced in Aliabadi and Tezduyar (1992), which is a modified version of the one described in Le Beau et al. (1992). The formulation based on the entropy variables is same as the one introduced in Hughes et al. (1986). The two formulations are tested on three different problems: adiabatic flat plate at Mach 2.5, Reynolds number 20,000; Mach 3 compression corner at Reynolds number 16,800; and Mach 6 NACA 0012 airfoil at Reynolds number 10,000. In all cases, we show that the results obtained with the two formulations are very close. This observation is the same as the one we had in Le Beau et al. (1992) for inviscid flows. © 1993 Springer-Verlag.

[ 3]

S. Mittal, A. Ratner, D. Hastreiter, and T.E. Tezduyar, “Space–time finite element computation of incompressible flows with emphasis on flows involving oscillating cylinders”, International Video Journal of Engineering Research, 1 (1991) 83–96
@ARTICLE{Mittal91b, AUTHOR = {S.~Mittal and A.~Ratner and D.~Hastreiter and T. E.~Tezduyar}, PAGES = {83--96}, JOURNAL = {International Video Journal of Engineering Research}, VOLUME = {1}, TITLE = {Space--Time Finite Element Computation of Incompressible Flows with Emphasis on Flows Involving Oscillating Cylinders}, YEAR = {1991} }

[ 2]

Y.J. Park, H.A. Deans, and T.E. Tezduyar, “Thermal effects on single-well chemical tracer tests for measuring residual oil saturation”, SPE Formation Evaluation, 6 (1991) 401–408, 10.2118/19683-PA
@ARTICLE{Park91a, AUTHOR = {Y. J.~Park and H. A.~Deans and T. E.~Tezduyar}, PAGES = {401--408}, JOURNAL = {SPE Formation Evaluation}, VOLUME = {6}, TITLE = {Thermal Effects on Single-Well Chemical Tracer Tests for Measuring Residual Oil Saturation}, YEAR = {1991}, DOI = {10.2118/19683-PA} } Abstract:
The single-well chemical-tracer (SWCT) test for measuring residual oil saturation, Sor, often involves injecting cool fluid containing a reactive tracer into a warm formation. The Sor estimation with this method depends on the separation between reactant and product tracers. Because the reaction rate is temperature-dependent, accounting for the thermal effects may be necessary to obtain reliable results. Two simulator models are normally used to interpret SWCT tests. The ideal model is used for relatively homogeneous sandstone formations. The pore-diffusion model is used for heterogeneous carbonate formations. Both models have now been solved with appropriate heat-balance equations. These nonisothermal models have been used to reinterpret several previously reported field tests. For the worst case, the estimated Sor value from the nonisothermal model is 5% PV higher than that from the isothermal model. Inequality conditions have been developed that divide the parameter space of SWCT tests into two regions, depending on the location of the temperature front relative to the tracer bank during the reaction period. In the 'safe' region, the estimated Sor values from isothermal and nonisothermal models are essentially equal. The inequality conditions have been extended to include the effects of over-and underburden layers and intervening shales in layered systems.

[ 1]

M. Behr, T.E. Tezduyar, and H. Higuchi, “Wake interference behind two flat plates normal to the flow: A finite-element study”, Theoretical and Computational Fluid Mechanics, 2 (1991) 223–250, 10.1007/BF00271639
@ARTICLE{Behr91a, AUTHOR = {M.~Behr and T. E.~Tezduyar and H.~Higuchi}, PAGES = {223--250}, JOURNAL = {Theoretical and Computational Fluid Mechanics}, VOLUME = {2}, TITLE = {Wake Interference Behind Two Flat Plates Normal to the Flow: {A}~Finite-Element Study}, YEAR = {1991}, DOI = {10.1007/BF00271639} } Abstract:
A finite-element model of the Navier-Stokes equations is used for numerical simulation of flow past two normal flat plates arranged side by side at Reynolds number 80 and 160. The results from this simulation indicate that when the gap between the plates is twice the width of a single plate, the individual wakes of the plates behave independently, with the antiphase vortex shedding being dominant. At smaller gap sizes, the in-phase vortex shedding, with strong wake interaction, is favored. The gap flow in those cases becomes biased, with one of the wakes engulfing the other. The direction of the biased flow was found to be switching at irregular intervals, with the time histories of the indicative flow parameters and their power spectra resembling those of a chaotic system. © 1991 Springer-Verlag.