On the homogenization of the Stokes problem in a perforated domain
Matthieu Hillairet · HAL (Le Centre pour la Communication Scientifique Directe) · 2016
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 aN tends to zero. Under the assumption that aN 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.