A Brinkman law in the homogenization of the stationary Navier-Stokes system in a non-periodic porous medium (Q2423543)

The authors study the asymptotic behavior of the Navier-Stokes system with Dirichlet boundary conditions posed in a bounded open set in 3D which is non-periodically perforated (prescribed randomness) by suitably small balls. Similarly to the periodic case, they obtain a limit system corresponding to a Brinkman flow. The main difference is that now the Brinkman matrix is not homogeneous, it depends on the density of the closed sets composing the perforations. The two-scale convergence method is slightly modified to handle this situation.