Communications in Mathematical Sciences

Volume 13 (2015)

Number 1

An ellipsoidal statistical model for gas mixtures

Pages: 1 – 13



Stéphane Brull (Université Bordeaux, IMB, Talence, France)


In this paper, we propose a construction of a new BGK model generalizing the Ellipsoidal Statistical Model [P. Andries, P. LeTallec, J.P. Perlat, B. Perthame, Eur. J. Mech. (B fluids), 19, 813–830, 2000], [L.H. Holway, Phys. Fluids, 9, 1958–1673, 1966] to the context of gas mixtures. The derivation of the model is based on the introduction of relaxation coefficients associated to some moments and the resolution of a minimization problem as in [S. Brull, J. Schneider, Cont. Mech. Thermodyn., 20(2), 63–74, 2008], [S. Brull, J. Schneider, Cont. Mech. Thermodyn., 20(8), 489–508, 2009], [S. Brull, V. Pavan, J. Schneider, Eur. J. Mech. (B-Fluids), 33, 74–86, 2012]. We obtain in this work an ESBGK model for gas mixtures satisfying the fundamental properties of the Boltzmann collision operator (conservation laws, H theorem, equilibrium states, …) and that is able to give a range of Prandtl numbers including the indifferentiability situation.


kinetic theory, gas mixtures, BGK models, moments systems

2010 Mathematics Subject Classification

35Q20, 35Q35

Published 16 July 2014