期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 75, 期 5, 页码 2001-2023出版社
SIAM PUBLICATIONS
DOI: 10.1137/14100110X
关键词
kinetic equation; Boltzmann equation; moment method; model reduction; hyperbolicity
资金
- Alexander von Humboldt Research Fellowship - Alexander von Humboldt Foundation of Germany
- National Basic Research Program of China [2011CB309704]
- National Natural Science Foundation of China [11325102, 91330205]
Through a deep investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for the Boltzmann equation in [Z. Cai, Y. Fan, and R. Li, Commun. Math. Sci., 11 (2013), pp. 547-571], we propose a uniform framework for the derivation of reduced models from general kinetic equations. The resulting model appears as a symmetric hyperbolic moment system. This reveals the underlying reason why some models in the literature are hyperbolic while others are not. This framework provides a simple flow chart, following which a number of existing models can be derived in a new way. The framework is also helpful in discovering new models. We apply this to Grad's 13-moment distribution function and obtain a new 13-moment model with global hyperbolicity.
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