Is the Lattice Boltzmann Method Applicable to Rarefied Gas Flows? Comprehensive Evaluation of the Higher Order Models

Abstract

Lattice Boltzmann method (LBM) whose equilibrium distribution function contains higherorder terms is called higherorder LBM. It is expected that nonequilibrium physics beyond the Navier–Stokes can be accurately captured using the higherorder LBM. Relationship between the level of higherorder and the simulation accuracy of rarefied gas flows is studied. Theoretical basis for constructing higherorder LBM is presented. On this basis, specific higherorder models are constructed. To confirm that the models have been correctly constructed, verification simulations are performed focusing on the continuum regime: sound wave and supersonic flow in Laval nozzle. With applications to microelectromechanical systems (MEMS) in mind, low Mach number flows are studied. Shear flow and heat conduction between parallel walls in the slip flow regime are investigated to confirm the relaxation process in the Knudsen layer. Problems between concentric cylinders are investigated from the slip flow regime to the free molecule regime to confirm the effect of boundary curvature. The accuracy is discussed comparing the simulation results with pioneers' studies. Models of the fourthorder give sufficient accuracy even for highly rarefied gas flows. Increase of the particle directions is necessary as the Knudsen number increases.