Effective coupling conditions for arbitrary flows in Stokes-Darcy systems

Abstract

Boundary conditions at the interface between the free-flow region and the adjacent porous medium is a key issue for physically consistent modeling and accurate numerical simulation of flow and transport processes in coupled systems due to the interface driven nature of such processes. Interface conditions available in the literature have several weak points: most of them are suitable only for flows parallel to the fluid-porous interface, some are restricted to specific boundary value problems, and others contain unknown model parameters which still need to be deter-mined. These facts severely restrict the variety of applications that can be successfully modeled. We propose new interface conditions which are valid for arbitrary flow directions. These coupling conditions are rigorously derived using the theory of homogenization and boundary layers. All effective parameters appearing in these conditions are computed numeri-cally based on the geometrical configuration of the coupled system. The developed conditions are validated by comparison of numerical simulation results for the coupled Stokes-Darcy model and the pore-scale resolved model. In addition, the new interface conditions are compared with the classical conditions to demonstrate the advantage of the proposed conditions.

Multiscale computational analysis of the Steady Multiscale Fluid Flow through a Lymph Node

“…Remark 1. We note that the Beavers-Joseph-Saffman boundary conditions were found experimentally in (Beavers and Joseph, 1967;Saffman, 1971) and demonstrated in Mikelić, 2000, 2009), but only in a 2D laminar case (as mentioned in (Auriault, 2010)), and the extension to a generic geometry is non-trivial (Eggenweiler and Rybak, 2021). Moreover, in (Auriault, 2010) they found that the corrector of the simplified boundary condition (12) is ϵ 2 .…”