HIGH ORDER SEMI-LAGRANGIAN METHODS FOR THE BGK EQUATION

被引：31

作者：

Groppi, Maria ^{[1
]}

Russo, Giovanni ^{[2
]}

Stracquadanio, Giuseppe ^{[1
]}

机构：

[1] Univ Parma, Dept Math & Comp Sci, I-43100 Parma, Italy

[2] Univ Catania, Dept Math & Comp Sci, I-95124 Catania, Italy

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2016年 / 14卷 / 02期

关键词：

Boltzmann equation; BGK equation; semi-Lagrangian methods; high-order schemes; RAREFIED-GAS DYNAMICS; KINETIC-EQUATIONS; BOLTZMANN-EQUATION; EXPLICIT SCHEMES; PART II; MODEL; MIXTURES;

D O I：

10.4310/CMS.2016.v14.n2.a4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new class of high-order accuracy numerical methods for the BGR model of the Boltzmann equation is presented. The schemes are based on a semi-Lagrangian formulation of the BGK equation; time integration is dealt with DIRK (Diagonally Implicit Runge-Kutta) and BDF methods; the latter turn out to be accurate and computationally less expensive than the former. Numerical results and examples show that the schemes are reliable and efficient for the investigation of both rarefied and fluid regimes in gas dynamics.

引用

页码：389 / 414

页数：26

共 30 条

[1] A hybrid method for hydrodynamic-kinetic flow - Part II - Coupling of hydrodynamic and kinetic models [J].

Alaia, Alessandro ;

Puppo, Gabriella .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (16) :5217-5242

[2] A consistent BGK-type model for gas mixtures [J].

Andries, P ;

Aoki, K ;

Perthame, B .

JOURNAL OF STATISTICAL PHYSICS, 2002, 106 (5-6) :993-1018

[3] Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations [J].

Ascher, UM ;

Ruuth, SJ ;

Spiteri, RJ .

APPLIED NUMERICAL MATHEMATICS, 1997, 25 (2-3) :151-167

[4] A MODEL FOR COLLISION PROCESSES IN GASES .1. SMALL AMPLITUDE PROCESSES IN CHARGED AND NEUTRAL ONE-COMPONENT SYSTEMS [J].

BHATNAGAR, PL ;

GROSS, EP ;

KROOK, M .

PHYSICAL REVIEW, 1954, 94 (03) :511-525

[5] Kinetic Bhatnagar-Gross-Krook model for fast reactive mixtures and its hydrodynamic limit [J].

Bisi, M. ;

Groppi, M. ;

Spiga, G. .

PHYSICAL REVIEW E, 2010, 81 (03)

[6] A weighted essentially nonoscillatory, large time-step scheme for Hamilton -Jacobi equations [J].

Carlini, E ;

Ferretti, R ;

Russo, G .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 27 (03) :1071-1091

[7]

Cercignani C., 1988, BOLTZMANN EQUATION I

[8] KINETIC-THEORETIC DESCRIPTION OF FORMATION OF A SHOCK WAVE [J].

CHU, CK .

PHYSICS OF FLUIDS, 1965, 8 (01) :12-&

[9] Towards an ultra efficient kinetic scheme. Part II: The high order case [J].

Dimarco, Giacomo ;

Loubere, Raphael .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 255 :699-719

[10]

Falcone M., 2014, Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations

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