Stokes flow in curved channels

In this paper, the problem of Stokes flow in curved channels is solved by applying the matched eigenfunction expansion method. The flow region is partitioned into a union of sectorial subregions. Then, within each subregion, the stream function is represented by an expansion of Papkovich–Fadle eigenfunctions. The coefficients in these expansions are obtained by requiring weak C3C3 continuity of the stream function across common interfaces. Biorthogonality conditions in cylindrical coordinates are utilized.