Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube

Abstract

Because of its mesoscopic nature and distinctive computing features, lattice Boltzmann method (LBM) is shown as a promising tool to simulate microscale gas flows. However, studies on the microtube flows are rare, and some fundamental problems for LBM to such flows still remain unsolved. In this work, three widely used kinetic boundary schemes, i.e., combined bounce-back and specular-reflection scheme, combined Maxwell-diffusion and specular-reflection scheme, and combined Maxwell-diffusion and bounce-back scheme, for the axisymmetric lattice Boltzmann equation (LBE) with multi-relaxation-time (MRT) are investigated. The discrete effects of the three boundary schemes in the axisymmetric MRT-LBE are observed by analyzing the micro-scale Hagen-Poiseuille flow, and the strategies of adjusting the parameters in the boundary schemes are put forward to implement the no-slip boundary condition and the second-order slip boundary condition. Some numerical tests are implemented to validate the proposed correction strategies for kinetic boundary schemes. Our analysis also shows that the kinetic boundary schemes of the axisymmetric Bhatnagar-Gross-Krook (BGK) LBE cannot realize the no-slip boundary condition and are also inapplicable to microscale gas flows with even some moderate Knudsen numbers (). Therefore, the axisymmetric MRT-LBE is superior to the axisymmetric BGK-LBE in realizing both the no-slip and slip boundary conditions.