Dans cette note, nous construisons un modèle de type ES–BGK pour des mélanges inertes, qui soit capable de donner un nombre de Prandl correct, correspondant à celui obtenu à partir de lʼéquation de Boltzmann. Le principe de construction est basé sur un principe de minimisation de lʼentropie sous contraintes, en introduisant une relaxation de certains moments non conservés. On obtient ainsi un modèle BGK capable de restituer un bon nombre de Prandtl dans certaines situations. De plus, le modèle construit vérifie les propriétés classiques satisfaites par lʼopérateur de Boltzmann pour les mélanges de gaz inertes.
In this note, we derive an ES–BGK model for gas mixtures that is able to give the correct Prandtl number obtained from the true Boltzmann equation. The derivation principle is based on the resolution of an entropy minimisation problem under moments constraints. The set of constraints is constructed by introducing a relaxation of some non-conserved moments. The non-conserved moments are dissipated according to some relaxation rates. Finally the BGK model that is obtained satisfies the classical properties of the Boltzmann operator for inert gas mixtures.
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Stéphane Brull 1
@article{CRMATH_2013__351_19-20_775_0, author = {St\'ephane Brull}, title = {Un mod\`ele {ES{\textendash}BGK} pour des m\'elanges de gaz}, journal = {Comptes Rendus. Math\'ematique}, pages = {775--779}, publisher = {Elsevier}, volume = {351}, number = {19-20}, year = {2013}, doi = {10.1016/j.crma.2013.04.006}, language = {fr}, }
Stéphane Brull. Un modèle ES–BGK pour des mélanges de gaz. Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 775-779. doi : 10.1016/j.crma.2013.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.04.006/
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