Breakdown of Chapman-Enskog expansion and the anisotropic effect for lattice-Boltzmann models of porous flow

Lattice-Boltzmann based models are frequently used to study fluid flow in porous media. The macroscopic governing equations as well as the viscosity and the permeability for such models are usually determined using a Chapman-Enskog expansion approach. However, this approach has been validated numerically only for a narrow range of the viscosity and the permeability. We have analytically derived the exact macroscopic governing equations of the lattice-Boltzmann model for the case of simple shear flows in porous media. We find that the effective viscosity in the governing equations is different from the one obtained from the Chapman-Enskog expansion. These findings have been validated numerically. We also find that the effective viscosity is anisotropic. Implications for modeling flow in porous media are discussed.