Two-fluid discrete Boltzmann model for compressible flows: based on Ellipsoidal Statistical Bhatnagar-Gross-Krook.

A 2-fluid Discrete Boltzmann Model(DBM) for compressible flows based on Ellipsoidal Statistical Bhatnagar-Gross-Krook(ES-BGK) is presented. The model has flexible Prandtl number and specific heat ratio. Mathematically, the model is composed of two coupled Discrete Boltzmann Equations(DBE). Each DBE describes one component of the fluid. Physically, the model is equivalent to a macroscopic fluid model based on Navier-Stokes(NS) equations, and supplemented by a coarse-grained model for thermodynamic nonequilibrium behaviours. To obtain a flexible Prandtl number, a coefficient is introduced in the ellipsoidal statistical distribution function to control the viscosity. To obtain a flexible specific heat ratio, a parameter is introduced in the energy kinetic moments to control the extra degree of freedom. Five typical benchmark tests are used to verify and validate the model. Some interesting nonequilibrium results, which are not available in the NS model or the single-fluid DBM, are presented.