  A two-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 or 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 non-equilibrium behaviors. 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. For binary mixture, the
correspondence between the macroscopic fluid model and the DBM may be
several-to-one. Five typical benchmark tests are used to verify and validate
the model. Some interesting non-equilibrium results, which are not available in
the NS model or the single-fluid DBM, are presented.
