Higher-order coupling conditions for arbitrary flows in Stokes-Darcy systems

TL;DR

This paper develops and rigorously analyzes higher-order interface conditions for coupling free-flow and porous-medium flow systems, improving accuracy over traditional conditions by accounting for arbitrary flow directions.

Contribution

It extends generalized coupling conditions for Stokes-Darcy systems and provides rigorous error estimates, validated through numerical simulations and pore geometry computations.

Findings

Higher-order interface conditions improve accuracy.

Numerical validation confirms theoretical error estimates.

Additional terms are significant for arbitrary flow directions.

Abstract

The choice of interface conditions for coupling free-flow and porous-medium flow systems is crucial in order to obtain accurate coupled flow models and precise numerical simulation results. Typically, the Stokes equations are considered in the free-flow region, Darcy's law is applied in the porous medium, and traditional coupling conditions (conservation of mass, balance of normal forces, the Beavers-Joseph condition on tangential velocity) are set on the interface. However, these traditional conditions are applicable to flows parallel to the fluid-porous interface only. Recently, we derived generalized interface conditions accounting for arbitrary flow directions to the porous layer using homogenization and boundary layer theory. We validated these conditions numerically and demonstrated that they are more accurate than the traditional coupling conditions. However, error estimates have not been derived yet. In this paper, we extend the generalized coupling conditions and prove rigorous error estimates for the homogenization result. All effective parameters appearing in the developed higher-order interface conditions are computed numerically based on the pore geometry. We validate the derived conditions by comparing numerical simulation results for the coupled Stokes-Darcy model and the pore-scale resolved model. Moreover, we compare the new coupling conditions to the traditional as well as generalized interface conditions and highlight the importance of the additional higher-order terms appearing in the derived coupling concept.