A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface

Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate modeling and simulation of various applications. To describe single-fluid-phase flows in coupled free-flow and porous-medium systems, the Stokes/Darcy equations are typically used together with the conservation of mass across the interface, the balance of normal forces and the Beavers-Joseph condition on the tangential velocity. The latter condition is suitable for flows parallel to the interface but not applicable for arbitrary flow directions. Moreover, the value of the Beavers-Joseph slip coefficient is uncertain. In the literature, it is routinely set equal to one that is not correct for many applications, even if the flow is parallel to the porous layer. In this paper, we reformulate the generalized interface condition on the tangential velocity component, recently developed for arbitrary flows in Stokes/Darcy systems, such that it has the same analytical form as the Beavers-Joseph condition. We compute the effective coefficients appearing in this modified condition using theory of homogenization with boundary layers. We demonstrate that the modified Beavers-Joseph condition is applicable for arbitrary flow directions to the fluid-porous interface. In addition, we propose an efficient two-level numerical algorithm based on simulated annealing to compute the optimal Beavers-Joseph parameter.