A BGK model for mixtures of monoatomic and polyatomic gases with discrete internal energy

We generalize the BGK model proposed in Bisi and Cáceres (2016) to a mixture constituted by both monoatomic and polyatomic gas species with each polyatomic one being characterized by its own number of discrete internal energy levels, to model its non-translational degrees of freedom. We prove that all disposable parameters appearing in the Maxwellian attractors may be determined in terms of the actual macroscopic fields in such a way that correct Maxwellian equilibria and collision invariants are preserved, as well as the validity of the H-theorem. Evolution equations for species densities, velocities and temperatures are also derived, and some numerical examples are shown in space homogeneous conditions.