For more information:
tezduyar@gmail.com

Flow in a Tube Constricted with a Flexible Diaphragm
A tube is constricted in the middle with a flexible diaphragm that has a hole (see Fig. 1). The fluid has properties similar to that of human blood. A pulsating inflow is specified in the form of a Cosine wave with period 0.3 s.
The numerical methods used in this computation were introduced and implemented on parallel computing platforms by the T*AFSM. The set of numerical methods introduced by the T*AFSM over the years and used in this computation includes the DSD/SST formulation [14], the quasidirect FSI method [5, 6], the stabilized spacetime FSI (SSTFSI) technique [7], and a number of special FSI techniques [7]. Among the special FSI techniques used in the computation is using split nodal values for pressure at the edges of the structure to stabilize the structure at those edges (see [7]). Another special computational fluid mechanics technique used here is preconditioning based on the segregated solver "Segregated Equation Solver for FluidStructure Interactions (SESFSI)" (see [7]). The computation was carried out on the ADA system at Rice University. For more details on this computation, see [7].

Fig. 1. Problem geometry. For details, see [7]. 


Fig. 2. Left: Volumetric flow rate for inflow and outflow. This shows that our computational technique yields a very good mass balance. Right: Displacement of the diaphragm at a point along its inner edge. For details, see [7]. 









Fig. 3. Time history (left to right and top to bottom) of the velocity field and pressure on a vertical plane. Velocity vectors are colored by magnitude. For details, see [7]. 
References
1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1992) 144.
2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces  The DeformingSpatialDomain/SpaceTime Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339351.
3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces  The DeformingSpatialDomain/SpaceTime Procedure: II. Computation of Freesurface Flows, Twoliquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353371.
4. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555575.
5. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "SpaceTime Techniques for Finite Element Computation of Flows with Moving Boundaries and Interfaces", Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Sciences, Monterrey, Mexico, CDROM (2004).
6. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "SpaceTime Finite Element Techniques for Computation of FluidStructure Interactions", Computer Methods in Applied Mechanics and Engineering, 195 (2006) 20022027.
7. T.E. Tezduyar and S. Sathe, "Modeling of FluidStructure Interactions with the SpaceTime Finite Elements: Solution Techniques", International Journal for Numerical Methods in Fluids, 54 (2007) 855900.
