A domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integrals

A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method based on Dirichlet-Neumann type splitting interface conditions solving separate Stokes Darcy problems iteratively. Second kind boundary integral equations are formulated each problem. use smoothing kernels that achieves high accuracy boundary, straightforward quadrature to discretize integrals. Numerical results demonstrate convergence, accuracy, dependence parameter values iterative problem viscous flow around porous sphere with known analytical solution, as well more general surfaces.