With the development of micro/nano-devices, low speed rarefied gas flows have attracted significant research interest where successful numerical methods for traditional high speed flows, including the direct simulation Monte Carlo method, become computationally too expensive. As the Knudsen number can be up to the order of unity in a micro/nano flow, one approach is to use continuum-based methods including the Navier-Stokes-Fourier (NSF) equations, Burnett/super Burnett equations, and moment models. Limited success has been achieved because of theoretical difficulties and/or numerical problems. The recently developed lattice Boltzmann equation (LBE) offers a fundamentally different approach which is close to kinetic methods but with a significantly smaller computational cost. However, success of LBE methods for rarefied gas motion has been mainly on isothermal flows. In this paper, thermal rarefied gas flows are investigated. Due to the unique features of micro/nano flows, a simplified thermal lattice Boltzmann model with two distribution functions can be used. In addition, kinetic theory boundary conditions for the number density distribution function can be extended to construct a thermal boundary condition. The model has been validated in the slip-flow regime against solutions of the NSF equations for shear and pressure driven flows between two planar plates. It is shown that the present thermal LBE model can capture some unique flow characteristics that the NSF equations fail to predict. The present work indicates that the thermal lattice Boltzmann model is a computationally economic method that is particularly suitable to simulate low speed thermal rarefied gas flows.
A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows