Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations

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Abstract
We present a thermal lattice Bhatnager-Gross-Krook (BGK) model in D-dimensional space for the numerical simulation of fluid dynamics. This model uses a higher-order velocity expansion for Maxwellian-type equilibrium distribution. In the meantime, the lattice symmetry has been upgraded to ensure isotropy for the six-order velocity-moment tensor. These manipulations lead to macroscopic equations without the nonlinear deviations, from which conventional thermal or nonthermal lattice BGK models suffered. We demonstrate the improvements by conducting classical Chapman-Enskog analysis and by the numerical calculation of the structure of the shock wave front and the decaying rate of the kinetic energy in the shear wave flow. Parameters in the velocity expansion are explicitly given for example models in one, two, and three dimensions. The transport coefficients of the modeled one-dimensional (1D) and 2D fluids are numerically measured as well.