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

Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic model

“…Such a result has not been achieved yet for the reactive case but it has been verified numerically to hold for the actual H-functional. The key point for the practical realization of this BGK approximation, which looks promising a priori and has proved satisfactory in several homogeneous and spacedependent applications, 19,20 is the availability of the exact Boltzmann exchange rates for mass, momentum, and energy. They are known in closed analytical form for the elastic scat-tering operator in the collision model of Maxwellian molecules, so that we will stick for simplicity also here to this common option.…”

“…To the authors' knowledge, deterministic reactive kinetic computations are restricted up to now to space-homogeneous scenarios 19 and to the one-dimensional Riemann problem. 20 This paper is aimed at investigating the steady shock wave problem in a reactive mixture by means of kinetic model equations of relaxation BGK type. Shock wave structure has attracted a lot of attention mainly for the inert prob-lem without chemical reactions and has been deeply studied in the frame of hydrodynamics 21 and extended thermodynamics.…”

On the validity of the Boltzmann-BGK model through relaxation evaluation

“…Thus, simple expressions have been proposed to replace the collision integral [2][3][4][5][6], and the resulting equation is called a model equation or kinetic model. A kinetic model enables the macroscopic laws to be derived from elementary principles and allows to deduce transport coefficients, which has arose renewed interests in the solution of model equations in recent years [7][8][9][10][11].…”

A Bhatnagar–Gross–Krook kinetic approach to fast reactive mixtures: Relaxation problems

“…There, it has been possible to prove that BGK equations retain most of the significant features of the Boltzmann equations: for instance, they preserve the correct collision invariants, conservation equations, and local equilibria (6) with mass action law (7). In addition, such a relaxation-time approximation, in spite of the heavy machinery of computing the auxiliary parameters in terms of the actual fields, turns out to be reliable in comparison to actual deterministic kinetic calculations in space homogeneous conditions [32], and to be effective in dealing with classical space dependent problems like steady shock structure [25] and Riemann problem [33]. However, there are some drawbacks which affect the previous BGK approach, and which confine its application to a partial range of the various physical parameters, on one side, and prevent a deeper mathematical investigation, on the other.…”