Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel

A wall equilibrium boundary condition for an implicit lattice-Boltzmann-equation method is proposed to simulate gas flows in a microchannel with rough surface on the characteristic length of gas molecules. The boundary condition is based on the assumption that impinging molecules reach equilibrium with the surface. The molecular mean free path used to define the Knudsen number is determined by the lattice speed and the relaxation time of the lattice-Boltzmann equation. With the wall equilibrium boundary condition and the appropriate relation defined for the Knudsen number and the relaxation time, the computed slip velocity and nonlinear pressure distribution along the microchannel are in excellent agreement with analytical solutions.