On the Homogenization of the Stokes Problem in a Perforated Domain - Hillairet, M. (Archive for rational mechanics and analysis, 2018)
We consider the Stokes equations on a bounded perforated domain completed with non-zero constant boundary conditions on the holes. We investigate configurations for which the holes are identical spheres and their number N goes to infinity while their radius a N tends to zero. Under the assumption that a N scales like a/N and that there is no concentration in the distribution of holes, we prove that the solution is well approximated asymptotically by solving a Stokes–Brinkman problem.