Analysis of the Stokes-Darcy problem with generalised interface conditions

TL;DR

This paper analyzes the Stokes-Darcy problem with generalized interface conditions derived for arbitrary flow directions, proving well-posedness and validating results through numerical studies for realistic applications.

Contribution

It provides the first mathematical proof of existence and uniqueness for the Stokes-Darcy problem with these new generalized interface conditions.

Findings

Existence and uniqueness of weak solutions established.

Well-posedness depends on permeability and boundary layer constants.

Numerical validation confirms theoretical results.

Abstract

Fluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many applications, fluid flow is non-parallel to the fluid-porous interface that requires a generalisation of the Beavers-Joseph coupling condition typically used for the Stokes-Darcy problem. Generalised coupling conditions valid for arbitrary flow directions to the interface are recently derived using the theory of homogenisation and boundary layers. The aim of this work is the mathematical analysis of the Stokes-Darcy problem with these generalised interface conditions. We prove the existence and uniqueness of the weak solution of the coupled problem. The well-posedness is guaranteed under a suitable relationship between the permeability and the boundary layer constants containing geometrical information about the porous medium and the interface. We numerically study the validity of the obtained results for realistic problems and provide a benchmark for numerical solution of the Stokes-Darcy problem with generalised interface conditions.