Homogenisation of the Stokes problem with a pure non-homogeneous slip boundary condition by the periodic unfolding method

Abstract

We study the homogenisation of the Stokes system with a non-homogeneous Fourier boundary condition on the boundary of the holes, depending on a parameter γ. Such systems arise in the modelling of the flow of an incompressible viscous fluid through a porous medium under the influence of body forces. At the limit, by using the periodic unfolding method in perforated domains, we obtain, following the values of γ, different Darcy's laws of typeMu= −N∇p+Fwith suitable matricesMandNwithFdepending on the right-hand side in the bulk term and in the boundary condition.