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 $L^2$ 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.