It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy's flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.
Prestininzi, P., Montessori, A., La Rocca, M., & Succi, S. (2016). Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy's flows. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 27(4), 1650037 [10.1142/S0129183116500376].