Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer

In this work, we apply the lattice Boltzmann equation (LBE) with multiple relaxation times (MRTs) to simulate the Poiseuille flow in the slip flow regime. We analyse in detail the discrete diffusive and combined bounce-back-specular-reflection boundary conditions for the LBE, the discrete effects at the boundary, and determinations of the relaxation times for the Poiseuille flow in the slip flow regime. In particular, we implement second-order slip boundary conditions with the MRT-LBE model and validate our numerical results for the slip Poiseuille flow with the Knudsen number Kn0.2 by using the analytic solution. Our analysis shows that the lattice Bhatnagar-Gross-Krook (BGK) model cannot yield correct results for the Poiseuille flow in the slip-flow regime. We also discuss the possibilities of extending the LBE for the Knudsen layer in micro flows.