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:nbn:de:hbz:386-kluedo-5264 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (127) Preprint English 1995 1995 Technische Universität Kaiserslautern 2000/04/03 Boltzmann Equation ; Numerical Simulation; Rarefied Gsa Dynamics Math. Mod. & Meth. Appl. Sci., Vol. 6, No. 1, 137-147 (1996) Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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.) Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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