  We derive a homogenized macroscopic model for fluid flows over ordered
homogeneous porous surfaces. The unconfined free-flow is described by the
Navier-Stokes equation, and the Darcy equation governs the seepage flow within
the porous domain. Boundary conditions that accurately capture mass and
momentum transport at the contact surface between these two domains are derived
using the multiscale homogenization technique. In addition to obtaining the
generalized version of the widely used Beavers-Joseph slip condition for
tangential velocities, the present work provides an accurate formulation for
the transpiration velocity and pressure jump at fluid-porous interfaces; these
two conditions are essential for handling two- and three-dimensional flows over
porous media. All the constitutive parameters appearing in the interface
conditions are computed by solving a set of Stokes problems on a much smaller
computational domain, making the formulations free of empirical parameters. The
tensorial form of the proposed interface conditions makes it possible to handle
flows over isotropic, orthotropic, and anisotropic media. A subset of interface
conditions, derived for porous media, can be used to model flows over rough
walls. The accuracy of the proposed macroscopic model is numerically quantified
for flows over porous and rough walls by comparing the results from our
homogenized model with those obtained from geometry-resolved microscopic
simulations.
