On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases

Céline Baranger; Marzia Bisi; Stéphane Brull; Laurent Desvillettes

doi:10.3934/krm.2018033

Article Contents

2018, Volume 11, Issue 4: 821-858. Doi: 10.3934/krm.2018033

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On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases

1.
CEA-CESTA, 15 avenue des sablières, CS 60001 33116 Le Barp Cedex, France
2.
University of Parma, Dept. of Mathematics, Physics and Computer Sciences, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
3.
University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France
4.
University Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, F-75013, Paris, France

^* Corresponding author: L. Desvillettes
^* Corresponding author: L. Desvillettes

Received: July 31, 2017

Revised: October 31, 2017

Published: April 2018

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Abstract

In this paper, we propose a formal derivation of the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic gases. We use a direct extension of the model devised in [8,16] for treating the internal energy with only one continuous parameter. This model is based on the Borgnakke-Larsen procedure [6]. We detail the dissipative terms related to the interaction between the gradients of temperature and the gradients of concentrations (Dufour and Soret effects), and present a complete explicit computation in one case when such a computation is possible, that is when all cross sections in the Boltzmann equation are constants.

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Mathematics Subject Classification: Primary: 76P05; Secondary: 82C40.

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