Interfacial conditions between a free-fluid region and a porous medium

Conditions at the dividing surface between a free-fluid and a porous region are of utmost importance when a two-domain approach is used to treat the coupled problem. Conditions arising from homogenization theory are derived here; they are akin to the classical Beavers-Joseph-Saffman conditions, the difference being that the coefficients which appear in the fluid-porous matching relations stem from the solution of microscopic, Stokes-like problems in a cell around the dividing surface with periodic conditions along the interface-parallel directions, and do not need to be fixed ad-hoc. The case of isotropic porous media is considered, and the model coefficients are provided for both two- and three-dimensional grains, for varying porosity. The relations at the interface are then tested for two problems: the stagnation-point flow over a porous bed and the motion past a backward-facing step, with the step region made of a porous material. To verify the accuracy of the conditions, macroscopic solutions are compared to feature-resolving simulations and excellent agreement is demonstrated, even for values of the Reynolds number larger than those for which the theory is formally applicable and for a large value of the porosity which results in significant infiltration of the fluid into the porous medium.