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Team for Advanced Flow Simulation and Modeling



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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 [1-4], the quasi-direct FSI method [5, 6], the stabilized space-time 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 Fluid-Structure 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) 1-44.

2. 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.

3. 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.

4. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555-575.

5. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "Space-Time 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, CD-ROM (2004).

6. 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.

7. 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.