Spectral collocation methods for Stokes flow in contraction geometries and unbounded domains

Abstract A spectral element method is described which enables Stokes flow in contraction geometries and unbounded domains to be solved as a set of coupled problems over semi-infinite rectangular subregions. Expansions in terms of the eigenfunctions of singular Sturm-Liouville problems are used to compute solutions to the governing biharmonic equation for the stream function. The coefficients in these expansions are determined by collocating the differential equation and boundary conditions and imposing C 3 continuity across the subregion interface. The suitability of domain truncation and algebraic mapping techniques are compared as well as the choice of trial functions.

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