Lattice Boltzmann Simulation of Micro-scale Gas Flows in the Transitional Regime

In order to study the flow characteristics of micro-scale gas in the transitional regime, the relationship between Knudsen number and dimensionless relaxation time was derived based on the gas kinetic theory and the effect of Knudsen layer. Computational formulas for the slip velocity on the wall and the bounce-back fraction were derived under a generalized second-order slip boundary condition using the boundary treatment method proposed by Succi. Then, a lattice Boltzmann model for micro-scale gas flows in the transitional regime was established, and the micro-scale Poiseuille flows in the transitional regime were simulated. Computational results show that when the rarefaction parameter is equal to 1.64, the computed dimensionless velocity profile is in good agreement with the dimensionless velocity profile given by Karniadakis in the whole transitional regime. The dimensionless velocity profile remains essentially a parabolic shape in the transitional regime. As Knudsen number increases, the dimensionless slip velocity rises in the boundary and falls in the center line.