A note on the lattice Boltzmann method beyond the Chapman-Enskog limits

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to Kn similar to O(1). This challenges the pessimistic stance, according to which the lattice Boltzmann method should only be used for strictly hydrodynamic purposes. It may also help the interpretation of recent simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.