Curved boundary conditions of the lattice Boltzmann method for simulating microgaseous flows in the slip flow regime

Abstract

The lattice Boltzmann method (LBM) has shown its promising capability in simulating microscale gas flows in the slip regime. However, the suitable boundary condition is still one of the critical issues for the LBM to model microgaseous flows involving curved geometries. In this paper, a local boundary condition of the LBM is proposed to treat curved solid walls of microgaseous flows in slip flow regime. The developed boundary treatment combines the Maxwellian diffuse reflection scheme (Ansumali and Karlin, 2002) and a single-node boundary scheme (Zhao et al., 2019) which contains a free parameter as well as the distance ratio. The curved boundary condition is analyzed within the multiple-relaxation-time (MRT) model for a unidirectional microflow. It is shown that the derived slip velocity depends on the free parameter as well as the distance ratio and relaxation times. By virtue of the free parameter, the combination parameter and the uniform relaxation time are theoretically determined to realize the accurate slip boundary condition. In addition, it is found that besides the halfway diffuse-bounce-back (DBB) scheme, previous curved boundary schemes only containing the distance ratio cannot ensure uniform relaxation times to realize the slip boundary condition. Some numerical examples with planar and curved boundaries are carried out to validate the present curved boundary scheme. The good and robust consistency of numerical predictions with analytical solutions demonstrates our theoretical analysis.