Lattice Boltzmann approach for the simulation of rarefied gas flow in the slip flow regime

Abstract

For rarefied gas flows in micro-devices, the rarefaction effect becomes significant and the slip at the solid wall becomes an important flow feature. The lattice Boltzmann equation (LBE) method has been used to simulate rarefied gas flows in micro-systems and proved its accuracy in capturing rarefied effect. However, the results of previous studies are not in accordance with each other even though they were started from the same governing equation to solve the same problem, and show only qualitative agreements with those of experimental or analytic approaches. The discrepancies of the results come from the boundary condition and the relation between Knudsennumber and relaxation-time. In this work, the best combination of LBE approach, which employs an equilibrium wall boundary condition and a Knudsen-number-relaxation-time relation derived using the viscosity-based mean free path and mean thermal speed, is suggested. The results of the simulations are compared with the analytic solutions. The present 2D results of microchannel and oscillatory shear-driven gas flows are in excellent agreement with the analytical solution. The results of 3D microchannel flow are also compared with the analytic solutions, and are in good agreement.