A penalization method to take into account obstacles in incompressible viscous flows

From the Navier-Stokes/Brinkman model, a penalization method has been derived by several authors to compute incompressible Navier-Stokes equations around obstacles. In this paper, convergence theorems and error estimates are derived for two kinds of penalization. The first one corresponds to a L-2 penalization inducing a Darcy equation in the solid body, the second one corresponds to a H-1 penalization and induces a Brinkman equation in the body. Numerical tests are performed to confirm the efficiency and accuracy of the method. Mathematics Subject Classification (1991): 76D99; 76S05.