SFB 1313 Publication "Justification of Generalized Interface Conditions for Stokes–Darcy Problems"

New SFB 1313 conference publication (International Conference on Finite Volumes for Complex Applications, FVCA 2023: Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems). The work has been developed within the SFB 1313 research project A03.

"Justification of Generalized Interface Conditions for Stokes–Darcy Problems"

Authors

• Elissa Eggenweiler (University of Stuttgart, SFB 1313 member)
• Joscha Nickl (University of Stuttgart, Aix-Marseille University)
• Iryna Rybak (University of Stuttgart, principal investigator of SFB 1313 research project A03)

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.