Derivation of a BGK model for reacting gas mixtures
type: Item
instance of: scholarly article
title: Derivation of a BGK model for reacting gas mixtures
zbMATH Open document ID: 1311.35176
author: Stéphane Brull
author: Jacques Schneider
published in: Communications in Mathematical Sciences
publication date: 2015-01-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q20
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N99
Mathematics Subject Classification ID: 76V05
zbMATH DE Number: 6384325
zbMATH Keywords: kinetic theory
zbMATH Keywords: gas mixtures
zbMATH Keywords: BGK models
zbMATH Keywords: entropy minimization
zbMATH Keywords: hydrodynamic limit
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: cms.2014.v12.n7.a2
OpenAlex ID: W2335346444
DOI: 10.4310/CMS.2014.V12.N7.A2
description: scientific article; zbMATH DE number 6384325