A Brinkman law in the homogenization of the stationary Navier-Stokes system in a non-periodic porous medium

Abstract We study the asymptotic behavior of the Navier–Stokes system with Dirichlet boundary conditions posed in a domain Ω e = Ω ∖ T e . Here Ω ⊂ R 3 is a bounded open set and T e is the union of many disjoint closed sets of size e 3 and density of order 1 ∕ e 3 , with e a small positive parameter. Similarly to the periodic case we get a limit system corresponding to a Brinkman flow. The difference is that now the Brinkman matrix is not homogeneous, it depends on the density of the closed sets composing T e . The result is obtained through an adaptation of the two-scale convergence method.