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Discrete effects on thermal boundary conditions for the thermal lattice Boltzmann method in simulating microscale gas flows

The lattice Boltzmann equation (LBE) has been shown to be able to describe important rarefied flow phenomena in the nearly continuum limit. However, the specific slip boundary condition for this promising method is still one of the critical issues. In this paper, two kinetic boundary conditions are proposed for simulating thermal microscale gas flows: one is the combination of the equilibrium distribution and specular-reflection scheme, another is the combination of the equilibrium distribution and bounce-back scheme. The two boundary conditions are then analyzed for the Couette flow. It is found that some discrete effects exist in the boundary conditions, which should be considered to ensure an accurate slip boundary condition. A correction method is then proposed to minimize the discrete effects, and numerical results demonstrate that the improved boundary schemes can yield much better results than the original ones.