Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow

The standard lattice Boltzmann equation (LBE) is inadequate for simulating gas flows with a large Knudsen number. In this paper we propose a generalized lattice Boltzmann equation with effective relaxation times based on a recently developed generalized Navier-Stokes constitution [Guo, Europhys Lett. 80, 24001 (2007)] for nonequilibrium flows. A kinetic boundary condition corresponding to a generalized second-order slip scheme is also designed for the model. The LBE model and the boundary condition are analyzed for a unidirectional flow, and it is found that in order to obtain the generalized Navier-Stokes equations, the relaxation times must be properly chosen and are related to the boundary condition. Numerical results show that the proposed method is able to capture the Knudsen layer phenomenon and can yield improved predictions in comparison with the standard lattice Boltzmann equation.