Boundary integral analysis for non-homogeneous, incompressible Stokes flows

Abstract

A regular-grid volume-integration algorithm has been previously developed for solving non-homogeneous versions of the Laplace and the elasticity equations. This note demonstrates that the same approach can be successfully adapted to the case of non-homogeneous, incompressible Stokes flow. The key observation is that the Stokeslet (Green’s function) can be written as $\mathcal {U}=\mu \nabla ^{2}\mathcal {H}$ , where $\mathcal {H}$ has a simple analytical expression. As a consequence, the volume integral can be reformulated as an easily evaluated boundary integral, together with a remainder domain integral that can be computed using a regular cuboid grid covering the domain.