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.Article Highlights A modification of the Beavers–Joseph condition is proposed based on recently developed generalized coupling conditions. The Beavers-Joseph parameter can be found only for unidirectional flows. An efficient numerical algorithm to determine the optimal Beavers-Joseph parameter is developed.
Physically consistent coupling conditions at the fluid-porous interface with correctly determined effective parameters are necessary for accurate mathematical modeling of various applications described by coupled free-flow and porous-medium problems. To model single-fluid-phase flows at low Reynolds numbers in such coupled systems, the Stokes/Darcy equations are typically used together with the conservation of mass across the fluid-porous interface, the balance of normal forces and the Beavers-Joseph condition on the tangential component of velocity. In the latter condition, the value of the Beavers-Joseph slip coefficient α BJ is uncertain, however, it is routinely set α BJ = 1 that is not correct for many applications. In this paper, three flow problems (pressure-driven flow, lid-driven cavity over porous bed, general filtration problem) with different pore geometries are studied. We determine the optimal value of the Beavers-Joseph parameter for unidirectional flows minimizing the error between the pore-scale resolved and macroscale simulation results. We demonstrate that the Beavers-Joseph slip coefficient is not constant along the fluid-porous interface for arbitrary flow directions, thus, the Beavers-Joseph condition is not applicable in this case.
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