An extended thermal Lattice Boltzmann model for transition flow

In the last two decades, mathematical models based on the Lattice Boltzmann method have been developed in an effort to accurately capture flow characteristics in rarefied conditions, including thermal effects. In order to improve their performance to characterize fluid conditions for the entire transition flow regime, a new wall-distance function has been developed based on existing Molecular Dynamics data and implemented to a D2Q13 Lattice Boltzmann model. The ability of the improved Lattice Boltzmann model to capture thermal effects on fluid conditions due to heat conduction and convection is demonstrated by simulating rarefied Fourier flow and Couette flow within micro/nano-channels, respectively, and validated against Direct Simulation Monte Carlo data as well as data based on the linearized Boltzmann equation. The results show that the proposed Lattice Boltzmann model is capable of simulating conditions, including thermal effects, in rarefied flow for the entire Knudsen number range representing slip, transition, and the low end of molecular flow regimes.