Lattice Boltzmann Method for Steady Gas Flows in Microchannels With Imposed Slip Wall Boundary Condition

Abstract

In this paper, we use a lattice Boltzmann method (LBM) for simulation of rarefied gas flows in microchannels at the slip flow regime. LBM uses D2Q9 lattice structure and BGK collision operator with single relaxation time. The solid wall boundary conditions used in this paper are based on the idea of bounceback of the non-equilibrium part of particle distribution in the normal direction to the boundary. The same idea is implemented at inlet and exit boundaries as well as at the wall surfaces. The distribution functions at the solid nodes are modified according to imposed density and slip velocity values at the wall boundaries. Simulation results are presented for microscale Couette and Poiseuille flows. The results are validated against analytical and/or experimental data for the slip velocity, nonlinear pressure drop and mass flow rate at various flow conditions. It was observed that the current application of LBM can accurately recover the physics of microscale flow phenomena in microchannels. The type of boundary treatment used in this study enables the implementation of coupled simulations where the flow properties at the regions near the wall can be obtained by other numerical methods such as the Direct Simulation Monte Carlo method (DSMC).