Reactive Euler equations of discrete models with reversible reactions

On the global well‐posedness of discrete Boltzmann systems with chemical reaction

“…Let us quote, for example, References [1][2][3] in the context of the full Boltzmann equation (BE), and References [4][5][6][7] in the context of the discrete Boltzmann equation (DBE). This discrete model consists of a system of hyperbolic semi-linear partial di erential equations describing the time-space evolution of a gas whose particles can attain a ÿnite number of preselected velocities only [8].…”

First-order kinetic approximation for a reactive gas mixture

“…Moreover, historical remarks, developments, relevant mathematical features, advantages and drawbacks of dvm for inert gases have been thoroughly outlined by Bobylev in his review paper [10]. For what concerns discrete and semi-continuous models, allowing also dissipative collisional processes, such as gas-photon interaction and chemical reactions, one may recall the recent papers [11], [12] by Schürrer et al and [13] by the present authors.…”

“…For this reason, it seems interesting to go further, extending the study of Ref. [13] to fluid dynamical processes with dissipative effects of viscosity, thermal conductivity and thermal diffusion due to chemical reactions. In the framework of dvm some previous efforts oriented in this sense are those of paper [14] for an inert gas and those of paper [15], where a bimolecular reaction and a Broadwell-type velocity discretization have been considered.…”

Kinetic Approach to Transport Properties of a Reacting Gas

“…Kinetic approaches to the study of gas mixtures with chemical reactions, have motivated several research works since the last decades, essentially based on Boltzmann-like models, as documented in paper [1] with reference to the full Boltzmann equation, and in paper [2] with reference to the discrete one. In the latter the mathematical theory concerning collision laws, chemical kinetics and thermodynamical equilibrium has been formulated for a kinetic model of a multicomponent mixture with general reversible reaction and velocity discretization.…”

“…where M is the space of mechanical-reactive collision invariants and F the space of mechanical collision invariants [2].…”