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Numerical Simulation of the Stationary One-Dimensional Boltzmann Equation by Particle Methods

  • The paper presents a numerical simulation technique - based on the well-known particle methods - for the stationary, one-dimensional Boltzmann equation for Maxwellian molecules. In contrast to the standard splitting methods, where one works with the instationary equation, the current approach simulates the direct solution of the stationary problem. The model problem investigated is the heat transfer between two parallel plates in the rarefied gas regime. An iteration process is introduced which leads to the stationary solution of the exact - space discretized - Boltzmann equation, in the sense of weak convergence.

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Author:Jens Struckmeier, A.V. Bobylev
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5279
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (128)
Document Type:Preprint
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Boltzmann Equation; Numerical Simulation; Rarefied Gas Dynamics
Source:Eur. J. Mech. B/Fluids, Vol. 15, No. 1, 103-118 (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