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Chebyshev pseudospectral method of viscous flows with corner singularities. (English) Zbl 0679.76042
Summary: Chebyshev pseudospectral solutions of the biharmonic equation governing two-dimensional Stokes flow within a driven cavity converge poorly in the presence of corner singularities. Subtracting the strongest corner singularity greatly improves the rate of convergence. Compared to the usual stream function/vorticity formulation, the single fourth-order equation for stream function used here has half the number of coefficients for equivalent spatial resolution and uses a simpler treatment of the boundary conditions. We extend these techniques to small and moderate Reynolds numbers.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
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