A BGK-Type Model for Multi-component Gas Mixtures Undergoing a Bimolecular Chemical Reaction

Abstract

We propose a new kinetic BGK-type model for a mixture of four monatomic gases, undergoing a bimolecular and reversible chemical reaction. The elastic and reactive interactions are described separately by distinct relaxation terms and the mechanical operator is the sum of binary BGK contributions, one for each pair of interacting species. In this way, our model separately incorporates the effects of mechanical processes and chemical reactions. Additionally, it retains the effects of inter-species interactions which are proper of the mixture. The dependence of Maxwellian attractors on the main macroscopic fields is explicitly expressed by assuming that the exchange rates for momentum and energy of mechanical and chemical operators coincide with the ones of the corresponding Boltzmann terms. Under suitable hypotheses, the relaxation of the distribution functions to equilibrium is shown through entropy dissipation. Some numerical simulations are included to investigate the trend to equilibrium.