The modeling of an incompressible fluid through a porous medium requires to deal with two systems of partial differential equations (PDEs) for the two types of media (fluid and porous). A possible way to couple theses two equations is by using the penalization approach. The latter consists in adding to the Navier- Stokes equations modeling the fluid flow a term simulating the porous medium, so that only one PDE has to be solved. The discretization in space is done by means of the finite element method (FEM), which will be suitably stabilized in order to employ equal order approximations for both the pressure and velocity variables. Finally, a passive flow control is analyzed.