Construction of BGK Models with a Family of Kinetic Entropies for a Given System of Conservation Laws |
| |
Authors: | Bouchut F. |
| |
Affiliation: | (1) Université d'Orléans et CNRS, UMR 6628, Département de Mathématiques, BP 6759, 45067 Orléans Cedex 2, France |
| |
Abstract: | We introduce a general framework for kinetic BGK models. We assume to be given a system of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK models that lead to this system in the hydrodynamic limit, and that are compatible with the whole family of entropies. This is obtained by a new characterization of Maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies. We deduce a general procedure to construct such BGK models, and we show how classical examples enter the framework. We apply our theory to isentropic gas dynamics and full gas dynamics, and in both cases we obtain new BGK models satisfying all entropy inequalities. |
| |
Keywords: | conservation laws BGK models hydrodynamic limit kinetic entropy space of maxwellians |
本文献已被 SpringerLink 等数据库收录! |
|