Communications in Mathematical Sciences

Volume 19 (2021)

Number 8

An ellipsoidal statistical model for a monoatomic and a polyatomic gas mixture

Pages: 2177 – 2194



Stéphane Brull (Institut de Mathématiques de Bordeaux, Université Bordeaux, Talence, France)


This paper is devoted to the derivation of an Ellipsoidal Statistical model for a mixture constituted by both monoatomic and polyatomic gases. The non-translational degrees of freedom are described by a continous variable and each polyatomic component is allowed to have its own internal degrees of freedom. The construction of the model is based on the moment relaxed method that has been developed in previous works and this method is generalized in the present paper to a more general setting. More precisely, this method is based on the introduction of free parameters and on the resolution of an entropy minimisation problem. The resulting model satisfies conservation properties and an $\mathrm{H}$ theorem. Next, by performing a Chapman–Engskog expansion, the model is shown to recover the right heat transfer coefficient, the shear viscosity and the volume viscosity.


BGK models, polyatomic mixture, hydrodynamic limit

2010 Mathematics Subject Classification

76P05, 82B40, 82D05

Received 27 August 2020

Accepted 9 May 2021

Published 7 October 2021