Derivation of a BGK model for reacting gas mixtures
After a short review of different Boltzmann equations for reacting mixtures the authors show that the construction of a new relaxation mechanical model can be achieved either at the of experimental values (Fick law) or by algorithms developed by \textit{A. Ern} and \textit{V. Giovangigli} [Multicomponent transport algorithms. Berlin: Springer (1994; Zbl 0820.76002)]. Special attention is payed to the definition of the relaxation coefficients for the chemical model. Then it is shown that the whole relaxation model satisfies the \(H\)-theorem and that the equilibrium states are Maxwellian functions, which densities and temperature are bound together with the mass action law. The conclusive section is devoted to the derivation of the Euler and the Navier-Stokes system in the slow reacting system. The Chapman-Enskog procedure yields the first formulation of the Navier-Stokes and computation of the chemical terms of the first order.
scientific article; zbMATH DE number 6384325