Derivation of a BGK model for mixtures

Stéphane Brull (1) , Vincent Pavan (2) , Jacques Schneider (3)

1 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux
2 IUSTI - Institut universitaire des systèmes thermiques industriels
3 IMATH - Institut de Mathématiques de Toulon - EA 2134

The aim of this article is to construct a BGK operator for gas mixtures starting from the true Navier-Stokes equations. That is the ones with transport coefficients given by the hydrodynamic limit of the Boltzmann equation(s). Here the same hydrodynamic limit is obtained by introducing relaxation coefficients on certain moments of the distribution functions. Next the whole model is set by using entropy minimization under moment constraints as in Brull and Schneider (2008. 2009) [23,24]. In our case the BGK operator allows to recover the exact Fick and Newton laws and satisfy the classical properties of the Boltzmann equations for inert gas mixtures. (C) 2012 Elsevier Masson SAS. All rights reserved.

Domaines: Physique [physics]

Stéphane Brull, Vincent Pavan, Jacques Schneider. Derivation of a BGK model for mixtures. European Journal of Mechanics - B/Fluids, 2012, 33, pp.74-86. ⟨10.1016/j.euromechflu.2011.12.003⟩. ⟨hal-01459970⟩