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.
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页码：1087 / 1114
页数：28
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