Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows

Abstract

We present mesoscopic fluid-wall interaction models for lattice Boltzmann (LB) model simulations of microscale flows. The exact solution of the slip velocity for the LB equation with the Bhatnagar-Gross-Krook collision operator is obtained for Poiseuille flow at finite Knudsen numbers. With a consistent definition of the Knudsen number, the slip coefficients of the LB equation with the standard D2Q9 scheme are found to be slightly larger than those of the Boltzmann equation with the same boundary condition, which makes the standard LB method remain quantitatively accurate only for small Knudsen numbers. By modifying the nonequilibrium energy flux or introducing the effective relaxation time, the LB method is analytically shown to reproduce the slip phenomena up to second order in the Knudsen number. For the standard LB method, the Knudsen layer is captured only with modification of the relaxation dynamics such as in the effective relaxation time model.