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

TL;DR

This paper introduces a boundary integral domain decomposition method for solving the 3D coupled Stokes-Darcy system with high accuracy, utilizing boundary integral equations and iterative solutions, validated through numerical experiments.

Contribution

It presents a novel boundary integral domain decomposition framework for the 3D Stokes-Darcy system, achieving high accuracy and robustness in numerical solutions.

Findings

Demonstrates convergence and accuracy of the method

Shows effectiveness for flow around porous spheres

Analyzes parameter dependence of iterative solutions

Abstract

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