Higher-Order Homogenized Boundary Conditions for Flows Over Rough and Porous Surfaces

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