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Subsonic Flow Past a Sphere

This 3D problem is solved for a set of Reynolds numbers ranging from 30 to 200 to demonstrate the reliability of compressible finite element flow solver at low Mach number flows. Here the Reynolds number is based on the free-stream values and the diameter of the sphere. The free-stream Mach number is 0.1. The figure shows the pressure distribution on the sphere and in the symmetry plane. Computed drag coefficients compare very well with the experimental values.

The mesh used to solve this problem consists of 148,969 nodes and 142,364 hexahedral elements. An explicit time integration method is used to obtain the solution of the coupled nonlinear system with 720,657 unknowns at every time step. This problem is solved on a CM-5 with 512 PNs. A similar set of simulations were performed later at higher resolution for Reynolds numbers between 10 to 400. At Reynolds number 400, 3D vortex shedding with a nondimensional frequency comparable to the experimental value was obtained. The mesh generator, flow solver, and flow visualization software (based on Visual3 library) were developed by the T*AFSM.


1. T.E. Tezduyar and T.J.R. Hughes, "Finite Element Formulations for Convection Dominated Flows with Particular Emphasis on the Compressible Euler Equations", AIAA Paper 83-0125, Proceedings of AIAA 21st Aerospace Sciences Meeting, Reno, Nevada (1983).

2. 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.

3. G.J. Le Beau and T.E. Tezduyar, "Finite Element Computation of Compressible Flows with the SUPG Formulation", Advances in Finite Element Analysis in Fluid Dynamics (eds. M.N. Dhaubhadel, M.S. Engelman and J.N. Reddy), FED-Vol. 123, ASME, New York (1991) 21-27.

4. 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.

5. 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.