Abstract
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 Kn ≤ 0.2 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.
Acknowledgements
Z.G. is grateful to Prof. L.-S. Luo for providing the reference by Verhaeghe et al. (Citation2007) before its publication and Prof. W.A. Yong for helpful discussions. This work is supported by the National Natural Science Foundation of China (50606012) and the National Basic Research Programme of China (under Grant No. 2006CB705804).