A double-distribution-function lattice Boltzmann model for high-speed compressible viscous flows

A lattice Boltzmann model for high-speed compressible viscous flows is presented based on the double-distribution-function lattice Boltzmann method proposed by Li et al. (2007). The D2Q17 circle function is introduced to take into account first to fourth order constraints of density equilibrium distribution function, in order for better consistency in the heat flux and the energy dynamics. The corresponding total energy equilibrium distribution function is formed. The present model is tested through three problems, i.e., the Riemann problem, regular shock reflection problem and supersonic boundary layer problem. We also observe improved performance of the new model for a supersonic boundary layer problem in comparison to the original coupled double-distribution-function lattice Boltzmann method.