Second Order Scheme for the Spatially Homogeneous Boltzmann Equation with Maxwellian Molecules

  • In the standard approach, particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction of the discretization parameter as well as on the differential cross section in the case of the general Boltzmann equation. Recently, it was shown, how to construct an implicit particle scheme for the Boltzmann equation with Maxwellian molecules. The present paper combines both approaches using a linear combination of explicit and implicit discretizations. It is shown that the new method leads to a second order particle method, when using an equiweighting of explicit and implicit discretization.

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Author:Jens Struckmeier, Konrad Steiner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5264
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (127)
Document Type:Preprint
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Tag:Boltzmann Equation ; Numerical Simulation; Rarefied Gsa Dynamics
Source:Math. Mod. & Meth. Appl. Sci., Vol. 6, No. 1, 137-147 (1996)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):65C05 Monte Carlo methods
76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
82C80 Numerical methods (Monte Carlo, series resummation, etc.)

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