Analytic solution for a higher-order lattice Boltzmann method: Slip velocity and Knudsen layer

Abstract

We present the analysis of a higher-order lattice Boltzmann (LB) method based on the fourth-order Gauss-Hermite quadrature, with emphasis on the slip velocity and the Knudsen layer. The exact solution of the slip velocity for the higher-order LB equation is obtained for Poiseuille flows with finite Knudsen numbers. Due to increased accuracy in velocity space discretization, the higher-order scheme gives much improved slip coefficients as compared with the standard LB method based on the third-order Gauss-Hermite quadrature. A multiple relaxation time model is investigated to show the effects of the relaxation times for higher-order moments on the slip phenomena.