Singular Matched Eigenfunction Expansions for Stokes Flow around a Corner
Timothy N. Phillips · IMA Journal of Applied Mathematics · 1989
A singular matched eigenfunction expansion method is described for solving Stokes flow around a corner. The flow region is decomposed into a number of simpler rectangular subregions; this enables the stream function to be represented by means of an expansion of Papkovich-Fadle eigenfunctions in each of these subregions. The coefficients in these expansions are obtained by matching them across common interfaces in a weak sense. The resulting solution is used in a post-processing technique to determine the coefficients in the known locally convergent expansion of the stream function at reentrant and salient corners. A small number of terms in this expansion is necessary to produce accurate approximations.