A compressible thermal lattice boltzmann model with factorization symmetry

A fully compressible multispeed lattice Boltzmann model is introduced and numerically demonstrated to simulate compressible thermal flow. The equilibrium distribution functions are derived by a nonperturbative algebraic theory in coordinate symmetry product form to avoid complex polynomial expansion of the Maxwellian function and Gauss-Hermite quadrature. An important characteristic of the proposed model is that it can be easily extendied to a multidimentional model with factorization symmetry. For compressible flows, Sod shock tube, Couette flow, and high-Mach double-reflection compressible flow are carried out to validate the present model for compressible flow and heat transfer. Numerical results are in excellent agreement with the theoretical solutions of fluid flows.