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3D Computation of Long-Wake Flows Behind Circular Cylinders

The multi-domain method, developed to address a challenging Army application (see Aerodynamics of a Parachute Crossing the Far Wake of an Aircraft), has also benefited 3D simulation of a classical problem: unsteady wake flow behind a circular cylinder. At Reynolds number 140, using three subdomains, we computed the wake flow as far as 300 diameters downstream. SD-2 and SD-3 contain no objects and are covered with structured meshes. Computations were carried out on a CRAY T3E-1200, and involved, at every time step of the simulation, solution of coupled, nonlinear equation systems with more than 0.8 million unknowns for SD-1, and more than 17 million unknowns for each of SD-2 and SD-3. We were able to extend our computations sufficiently downstream, and with sufficient accuracy, to successfully capture (in SD-3) 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.


1. T.J.R. Hughes, T.E. Tezduyar and A.N. Brooks, "Streamline Upwind Formulations for Advection-Diffusion, Navier-Stokes, and First-order Hyperbolic Equations", Proceedings of the Fourth International Conference on Finite Element Methods in Fluid Flow, University of Tokyo Press, Tokyo (1982).

2. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1991) 1-44.

3. 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.

4. S. Mittal and T.E. Tezduyar, "A Finite Element Study of Incompressible Flows Past Oscillating Cylinders and Airfoils", International Journal for Numerical Methods in Fluids, 15 (1992) 1073-1118.

5. V. Kalro and T. Tezduyar, "Parallel 3D Computation of Unsteady Flows around Circular Cylinders", Parallel Computing, 23 (1997) 1235-1248.

6. T. Tezduyar and Y. Osawa, "Methods for Parallel Computation of Complex Flow Problems", Parallel Computing, 25 (1999) 2039-2066.