  We study the fluid flow through disordered porous media by numerically
solving the complete set of the Navier-Stokes equations in a two dimensional
lattice with a spatially random distribution of solid obstacles (plaquettes).
We simulate viscous and non-viscous flow through these idealized pore spaces to
determine the origin of the deviations from the classical Darcy's law behavior.
Due to the non-linear contribution of inertia to the transport of momentum at
the pore scale, we observe a typical departure from Darcy's law at sufficiently
high Reynolds numbers. Moreover, we show that the classical Forchheimer
equation provides a valid phenomenological model to correlate the variations of
the friction factor of the porous media over a wide range of Reynolds
conditions.
