Cellular-automata calculation of frequency-dependent permeability of porous media

We use a cellular-automata (CA) method to determine the frequency-dependent permeability k(ω) of a channel and a disordered porous medium. The CA results for the channel flow agree completely with the analytical solution of the problem. For flow in a porous medium, we calculate k(ω) over a wide range of the frequencies ω and for several values of the porosity. Our CA results for disordered porous media support the relation k(ω)/${\mathit{k}}_0$=f(ω/${\mathrm{\omega }}_{\mathit{c}}$), where ${\mathit{k}}_0$ is the static permeability of the medium, ${\mathrm{\omega }}_{\mathit{c}}$ is a characteristic frequency, and f(x) is a universal function, proposed previously, based on experimental data.