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Implicit and Iterative Methods for the Boltzmann Equation

  • The paper presents some approximation methods for the Boltzmann equation. In the first part fully implicit discretization techniques for the spatially homogeneous Boltzmann equation are investigated. The implicit equation is solved using an iteration process. It is shown that the iteration converges to the correct solution for the moments of the distribution function as long as the mass conservation is strictly fulfilled. For a simple model Boltzmann equation some unexpected features of the implicit scheme and the corresponding iteration process are clarified. In the second part a new iteration algorithm is proposed which should be used for the stationary Boltzmann equation. The realization of the method is very similar to the standard splitting algorithms except some new stochastic elements.

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Author:A.V. Bobylev, Jens Struckmeier
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5220
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (123)
Document Type:Preprint
Language of publication:English
Year of Completion:1994
Year of Publication:1994
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Boltzmann Equation; Numerical Simulation; Rarefied Gas Dynamics
Source:TTSP, Vol. 25, No. 2, 175-195 (1996)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Pxx Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] / 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C80 Numerical methods (Monte Carlo, series resummation, etc.)
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011