Lattice Boltzmann models for non-equilibrium gas flows

Due to its computational efficiency, the kinetic-based lattice Boltzmann method has recently been used to model nonequilibrium gas dynamics. With appropriate boundary conditions, lattice Boltzmann models have been able to capture both velocity slip and temperature jump at a solid surface. To enable these models to simulate flows in the transition regime, both high-order and modified lattice Boltzmann models have been proposed. In this paper, we demonstrate the advantages of the standard lattice Bhatnagar-Gross-Krook model in predicting high-order rarefaction phenomenon. In addition, we show that current high-order lattice Boltzmann models are not yet able to capture the nonlinear constitutive relation for the stress in the Knudsen layer, despite the improved predictions of the wall slip-velocity, especially for Poiseuille flow. By considering how the wall affects the gas mean free path, we present a simplified high-order lattice Boltzmann model that can predict flow in the transition regime and is also able to capture the essential characteristics of the Knudsen layer.