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# Communications in Mathematical Sciences

## Volume 13 (2015)

### Number 5

### A well-posed simulation model for multicomponent reacting gases

Pages: 1075 – 1103

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n5.a2

#### Author

#### Abstract

We aim to present a relaxation model that can be used in real simulations of dilute multicomponent reacting gases. The kinetic framework is the semi-classical approach with only one variable for the internal energy modes. The relaxation times for the internal energy modes are assumed to be smaller than the chemistry characteristic times. The strategy is the same as in [S. Brull and J. Schneider, *Commun. Math. Sci.,* 12, 1199–1223, 2014]. That is, a sum of operators for respectively the mechanical and chemical processes. The mechanical operator(s) is the “natural” extension to polyatomic gases of the method of moment relaxations presented in [S. Brull and J. Schneider, *Cont. Mech. Thermodyn.* 20(2), 63–74, 2008] [S. Brull, V. Pavan, and J. Schneider, *Eur. J. Mech. (B-Fluids),* 33, 74–86, 2012]. The derivation of the chemical model lies on the chemical processes at thermal equilibria. It is shown that this BGK approach features the same properties as the Boltzmann equation: conservations and entropy production. Moreover, null entropy production states are characterized by vanishing chemical production rates. We also study the hydrodynamic limit in the slow chemistry regime. Finally, we show that the whole set of parameters that are used in the derivation of the model can be calculated by softwares such as EGlib [A. Ern, V. Giovangigli, http://www.cmap.polytechnique.fr/www.eglib/ ] or STANJAN [B. Reynolds, http://www.stanford.edu/].

#### Keywords

kinetic theory, BGK models, polyatomic gases, chemical reactions, entropy production, hydrodynamic limit

#### 2010 Mathematics Subject Classification

35Q20, 35Q35

Published 22 April 2015