High-order lattice Boltzmann models for gas flow for a wide range of Knudsen numbers

The lattice Boltzmann methods (LBMs) have successfully been applied to microscale flows in the hydrodynamic regime, such as flows of liquids in porous media. However, the LBM in its standard formulation does not produce correct results beyond the hydrodynamic regime, i.e., for slip and transitional ones. Following the work of Shan and He [Phys. Rev. Lett. 80, 65 (1998)], we propose to extend the LBM to these regimes in which nonequilibrium effects are obvious and require us to include a larger number of distribution-function moments.