Stokes-Darcy boundary integral solutions using preconditioners

In a system where a free fluid flow is coupled to flow in a porous medium, different PDEs are solved simultaneously in two subdomains. We consider steady Stokes equations in the free region, coupled across a fixed interface to Darcy equations in the porous substrate. In this paper, the numerical solution is obtained using the boundary integral formulation with regularized Green’s function. Higher accuracy is achieved by applying a correction process, which also results in the improvement of the condition number of the linear system. In this work, an appropriate preconditioner based on the singular part of corrections is introduced to improve the convergence of a Krylov subspace method applied to solve the integral formulation.