A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids

An accurate Fourier-Chebyshev spectral collocation method has been develope d for simulating flow past prolate spheroids. The incompressible Navier-Sto kes equations are transformed to the 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 conven tional Fourier expansion is used in this direction. The other wall-tangenti al direction requires special treatment and a restricted Fourier expansion that satisfies the parity conditions across the poles is used. Issues inclu ding spatial and temporal discretization, efficient inversion of the pressu re Poisson equation, outflow boundary condition and stability restriction a t the pole are discussed. The solver has been validated primarily by simula ting steady and unsteady flow past a sphere at various Reynolds numbers and comparing key quantities with corresponding data from experiments and othe r numerical simulations. Copyright (C) 1999 John Wiley & Sons, Ltd.