HIGHER ORDER MIXED-MOMENT APPROXIMATIONS FOR THE FOKKER-PLANCK EQUATION IN ONE SPACE DIMENSION

被引：20

作者：

Schneider, Florian ^{[1
]}

Alldredge, Graham ^{[2
]}

Frank, Martin ^{[2
]}

Klar, Axel ^{[1
,3
]}

机构：

[1] TU Kaiserslautern, Fachbereich Math, D-67663 Kaiserslautern, Germany

[2] Rhein Westfal TH Aachen, Dept Math, Aachen, Germany

[3] Fraunhofer Inst Techno & Wirtschaftsmath, D-67663 Kaiserslautern, Germany

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2014年 / 74卷 / 04期

关键词：

partial differential equations; Fokker-Planck equations; methods of moments; minimum entropy; partial moments; hyperbolic partial differential equation; RADIATIVE HEAT-TRANSFER; ENTROPY-BASED CLOSURES; ELECTRON RADIOTHERAPY; EDDINGTON FACTORS; QUADRATURE METHOD; LINEAR TRANSPORT; RIEMANN SOLVERS; PARTICLE FLOWS; SLAB GEOMETRY; HIERARCHY;

D O I：

10.1137/130934210

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy M-n models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They provide nonnegative distribution functions combined with an analytical closure. Numerical tests are performed with standard first-order finite volume schemes and compared with a finite difference Fokker-Planck scheme.

引用

页码：1087 / 1114

页数：28

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