On the numerical solution of a BGK-type model for chemical reactions

In recent years, new suggestions and proposals concerning the mathematical modelling and applications of multi-component gaseous flows with chemical reactions have been published. A recent consistent BGK-type approach to reacting gas mixtures, according to Boltzmann-like kinetics for a bimolecular reversible chemical reaction has been introduced. In this paper we apply a numerical strategy based on time splitting techniques to simulate the reactive BGK equations. These techniques, widely used in the numerical approximation of the Boltzmann kinetic description, but not in the numerical analysis of the kinetic systems describing reacting gas mixtures, have the advantage of simplifying the problem by treating separately the convection step and collision step. Numerical tests of various splitting schemes on the classical BGK equation and several numerical results of the time-dependent Riemann problem for the reactive BGK system are presented.