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The lattice Boltzmann method has been successfully applied for the simulation of through porous media in the creeping regime. Its technical properties, namely discretization, straightforward implementation and parallelization, are responsible for its popularity. However, through porous is not restricted to near zero Reynolds numbers since inertial effects play a role in numerous natural and industrial processes. In this paper we investigate the capability of the lattice Boltzmann method to correctly describe in porous media at moderate Reynolds numbers. The selection of the lattice resolution, the collision kernel and the boundary conditions becomes increasingly important and the challenge is to keep artifacts due to compressibility effects at a minimum. The Boltzmann results show an accurate quantitative agreement with finite element method results and evidence the capability of the method to reproduce Darcy's law at low Reynolds numbers and Forchheimer's law at high Reynolds numbers.
Gray et al. (Tue,) studied this question.