Justification of Generalized Interface Conditions for Stokes–Darcy Problems

Abstract

For accurate modeling and numerical simulation of free-flow and porous-medium flow systems, the correct choice of coupling conditions at the common interface is essential. Most of the interface conditions available in the literature are limited to flows parallel or perpendicular to the porous layer. This significantly limits the number of applications that can be modeled in a physically meaningful way. Recently, generalized coupling conditions for arbitrary flow directions to the fluid–porous interface have been developed using homogenization and boundary layer theory. These conditions were validated numerically, however, their justification via error estimates was up to now an open question. In this work, we derive new interface conditions that extend the generalized coupling conditions by some higher-order boundary layer correctors. Under additional regularity and boundedness assumptions, we obtain error estimates that justify our newly developed coupling conditions.