On the approximation of kinetic equations by moment systems

  • The aim of this article is to show that moment approximations of kinetic equations based on a Maximum Entropy approach can suffer from severe drawbacks if the kinetic velocity space is unbounded. As example, we study the Fokker Planck equation where explicit expressions for the moments of solutions to Riemann problems can be derived. The quality of the closure relation obtained from the Maximum Entropy approach as well as the Hermite/Grad approach is studied in the case of five moments. It turns out that the Maximum Entropy closure is even singular in equilibrium states while the Hermite/Grad closure behaves reasonably. In particular, the admissible moments may lead to arbitrary large speeds of propagation, even for initial data arbitrary close to global eqilibrium.

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Author:Wolfgang Dreyer, Michael Junk, Matthias Kunik
URN (permanent link):urn:nbn:de:hbz:386-kluedo-10516
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (229)
Document Type:Preprint
Language of publication:English
Year of Completion:2000
Year of Publication:2000
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/08/17
Tag:Fokker-Planck equation ; Grad expansion ; exact solution ; maximum entropy ; moment methods ; moment realizability
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification (mathematics):82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C70 Transport processes
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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