## Team for Advanced Flow Simulation and Modeling |

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## 2-5 Spheres Falling in a Liquid Filled TubeThese simulations involve multiple spheres falling in a liquid filled tube. Between 2 to 5 spheres with different initial arrangements are allowed to fall with their dynamics determined by the fluid forces acting on them. They may also collide if any two spheres get too close to each other. Due to the requirement that there may be any number of spheres at any location, a 3D automatic mesh generator is used to discretize the domain. Also, due to the arbitrary motions of the spheres, a mesh moving scheme which handles the movement of the mesh automatically is used. In this scheme, the movement of the mesh is governed by the equations of linear elasticity. New meshes are created with the automatic mesh generator as often as needed to avoid reaching unacceptable levels of mesh distortion. In one of the simulations, there are two spheres initially in a staggered arrangement. As the spheres fall, the trailing sphere is attracted to the low-pressure region in the wake of the leading sphere. The two spheres eventually collide and then separate. The two spheres then fall side by side throughout the rest of the simulation. The location of the spheres at five instants during the simulation can be seen in the figure on the left. In another simulation, there are five spheres initially in a slightly jumbled pentagon arrangement. As the spheres fall, they eventually rearrange themselves into the exact pentagon arrangement which seems to be the most stable state for five spheres. The location of the spheres at five instants during the simulation can be seen in the figure on the right. Both the unstructured mesh generator and flow solver were developed by the T*AFSM. Movies of each of these simulations were also made.
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Incompressible Flow Computations", 2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for
Finite Element Computations Involving Moving Boundaries and
Interfaces--The DSD/ST Procedure: I. The Concept and the Preliminary
Numerical Tests", 3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New
Strategy for Finite Element Computations Involving Moving Boundaries
and Interfaces--The DSD/ST Procedure: II. Computation of Free-surface
Flows, Two-liquid Flows, and Flows with Drifting Cylinders",
4. A.A. Johnson and T.E. Tezduyar, "Simulation of Multiple
Spheres Falling in a Liquid-Filled Tube", 5. A.A. Johnson and T.E. Tezduyar, "3D Simulation of
Fluid-Particle Interactions with the Number of Particles Reaching
100", 6. T. Tezduyar, "CFD Methods for Three-Dimensional Computation
of Complex Flow Problems", 7. A. Johnson and T. Tezduyar, "Advanced Mesh Generation and
Update Methods for 3D Flow Simulations", 8. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation
of Complex Flow Problems", 9. A. Johnson and T.
Tezduyar, "Methods for 3D Computation of Fluid-Object Interactions in
Spatially-Periodic Flows", |