The coupling between the flow through a fibrous porous medium and that in a free-fluid region is studied. The flow dynamics inside the porous medium are described using the volume averaging method applied to the incompressible Navier−Stokes equations in the laminar regime. The two different flow domains are coupled via a penalization method that consists of varying the porous medium properties (porosity and permeability) continuously across the interface. This approach permits the use of the same set of the equations throughout the whole domain. The averaging method is validated against simulations which fully account for the presence of cylindrical fibers positioned at the bottom wall of a square driven cavity. Numerical experiments are carried out for two different Reynolds numbers, large enough to ensure that inertial effects inside the porous domain are not negligible. Good agreement is found when comparing the two approaches.