Inertial effects on fluid flow through disordered porous media

We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional dis ordered porous media. We apply the Forchheimer equation as a phenomenologic al model to correlate the variations of the friction factor for different p orosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition ca n be understood and statistically characterized in terms of the spatial dis tribution of kinetic energy in the system.