Inertial Effects on Fluid Flow through Disordered Media

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