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A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids. (English) Zbl 0957.76060
Summary: We develop a Fourier-Chebyshev spectral collocation method for simulating flows past prolate spheroids. The incompressible Navier-Stokes equations are written out in prolate spheroidal co-ordinate system and discretized on an orthogonal body-fitted mesh. The infinite flow domain is truncated to a finite extent, and a Chebyshev discretization is used in the wall-normal direction. The azimuthal direction is periodic, and a conventional Fourier expansion is used in this direction. The other wall-tangential direction requires special treatment, and here we use a restricted Fourier expansion that satisfies the parity conditions across the poles. We discuss spatial and temporal discretization, efficient inversion of pressure Poisson equation, outflow boundary condition and stability restriction at the pole. The solver has been validated by simulating steady and unsteady flow past a sphere at various Reynolds numbers, and by comparing key quantities with corresponding data from experiments and other numerical simulations.

MSC:
76M22 Spectral methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D25 Wakes and jets
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