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

共 50 条

[1] FIRST-ORDER QUARTER-AND MIXED-MOMENT REALIZABILITY THEORY AND KERSHAW CLOSURES FOR A FOKKER-PLANCK EQUATION IN TWO SPACE DIMENSIONS
Schneider, Florian
Roth, Andreas
Kall, Jochen
KINETIC AND RELATED MODELS, 2017, 10 (04) : 1127 - 1161
[2] On the higher order corrections to the Fokker-Planck equation
Plyukhin, A
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2005, 351 (2-4) : 198 - 210
[3] FOKKER-PLANCK EQUATION AND ITS DIFFUSION APPROXIMATIONS
ENGLADE, RC
BULLETIN OF THE AMERICAN PHYSICAL SOCIETY, 1971, 16 (12): : 1426 - &
[4] Higher order averaging method of coefficients in Fokker-Planck equation
Anh, ND
Tinh, ND
IUTAM SYMPOSIUM ON NONLINEARITY AND STOCHASTIC STRUCTURAL DYNAMICS, 2001, 85 : 1 - 14
[5] Higher order Fokker-Planck operators
Pomraning, GC
NUCLEAR SCIENCE AND ENGINEERING, 1996, 124 (03) : 390 - 397
[6] Angular moment model for the Fokker-Planck equation
B. Dubroca
J.-L. Feugeas
M. Frank
The European Physical Journal D, 2010, 60 : 301 - 307
[7] On the approximation of the Fokker-Planck equation by moment systems
Dreyer, W
Junk, M
Kunik, M
NONLINEARITY, 2001, 14 (04) : 881 - 906
[8] Angular moment model for the Fokker-Planck equation
Dubroca, B.
Feugeas, J. -L.
Frank, M.
EUROPEAN PHYSICAL JOURNAL D, 2010, 60 (02): : 301 - 307
[9] HIGHER-ORDER AVERAGING METHOD OF COEFFICIENTS IN FOKKER-PLANCK EQUATION
ANH, ND
SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES, 1995, 20 : 373 - 387
[10] Subspace approximations to the cosmic ray Fokker-Planck equation
Lasuik, J.
Shalchi, A.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 2019, 485 (02) : 1635 - 1650

← 1 2 3 4 5 →