Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method

We present a numerical method to solve the equations for low-Reynolds-number (Stokes) flow in porous media. The method is based on the lattice-Boltzmann approach, but utilizes a direct solution of time-independent equations, rather than the usual temporal evolution to steady state. Its computational efficiency is 1-2 orders of magnitude greater than the conventional lattice-Boltzmann method. The convergence of the permeability of random arrays of spheres has been analyzed as a function of mesh resolution at several different porosities. For sufficiently large spheres, we have found that the convergence is quadratic in the mesh resolution.