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Interfacial boundary conditions determined from empirical or ad-hoc modelsremain the standard approach to model fluid flows over porous media, even insituations where the topology of the porous medium is known. We propose anon-empirical and accurate method to compute the effective boundary conditionsat the interface between a porous surface and an overlying flow. Usingmultiscale expansion (homogenization) approach, we derive a tensorialgeneralized version of the empirical condition suggested by Beavers & Joseph(1967). The components of the tensors determining the effective slip velocityat the interface are obtained by solving a set of Stokes equations in a smallcomputational domain near the interface containing both free flow and porousmedium. Using the lid-driven cavity flow with a porous bed, we demonstrate thatthe derived boundary condition is accurate and robust by comparing an effectivemodel to direct numerical simulations. Finally, we provide an open source codethat solves the microscale problems and computes the velocity boundarycondition without free parameters over any porous bed.

A framework for computing effective boundary conditions at the interface between free fluid and a porous medium