Kinetic Bhatnagar-Gross-Krook model for fast reactive mixtures and its hydrodynamic limit

A recently proposed consistent BGK--type approach for reversible bimolecular chemical reactions, well suited to deal with collision dominated gas mixtures in which mechanical and chemical relaxation times are of the same order of magnitude (fast reactions), is discussed. The model recovers essential features of the chemical process like mass action law at equilibrium and reactive H-theorem. The hydrodynamic limit, at both Euler and Navier-Stokes level, is derived by a Chapman-Enskog procedure, in terms of the relevant hydrodynamic variables, and compared to the corresponding limits holding in the non-reactive and in the slowly reactive cases. In particular, results show that reactive corrections to transport coefficients can not be neglected for fast reactions.