BGK-type models in strong reaction and kinetic chemical equilibrium regimes

A BGK-type procedure is applied to multi-component gases undergoing chemical reactions of bimolecular type. The relaxation process towards local Maxwellians, depending on mass and numerical densities of each species as well as common velocity and temperature, is investigated in two different cases with respect to chemical regimes. These cases are related to the strong reaction regime characterized by slow reactions, and to the kinetic chemical equilibrium regime where fast reactions take place. The consistency properties of both models are stated in detail. The trend to equilibrium is numerically tested and comparisons for the two regimes are performed within the hydrogen–air and carbon–oxygen reaction mechanism. In the spatial homogeneous case, it is also shown that the thermodynamical equilibrium of the models recovers satisfactorily the asymptotic equilibrium solutions to the reactive Euler equations.