Approximation of mono-dimensional hyperbolic systems: A lattice Boltzmann scheme as a relaxation method

被引：20

作者：

Graille, B. ^{[1
,2
]}

机构：

[1] Univ Paris 11, Math Lab, UMR 8628, F-91405 Orsay, France

[2] CNRS, F-91405 Orsay, France

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 266卷

关键词：

Lattice Boltzmann scheme; Relaxation method; Hyperbolic system; FLOWS; MODEL;

D O I：

10.1016/j.jcp.2014.02.017

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We focus on mono-dimensional hyperbolic systems approximated by a particular lattice Boltzmann scheme. The scheme is described in the framework of the multiple relaxation times method and stability conditions are given. An analysis is done to link the scheme with an explicit finite differences approximation of the relaxation method proposed by Jin and Xin. Several numerical illustrations are given for the transport equation, Burger's equation, the p-system, and full compressible Euler's system. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：74 / 88

页数：15

共 26 条

[1]

[Anonymous], 1998, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, DOI 10.1007/BFb0096355

[2]

Aregba-Driollet D., 1996, APPL ANAL, V61, P163

[3]

Berthelin F, 2002, ASYMPTOTIC ANAL, V31, P153

[4]

Berthelin F., 2002, Methods Appl. Anal., V9, P313

[5] Momentum transfer of a Boltzmann-lattice fluid with boundaries [J].

Bouzidi, M ;

Firdaouss, M ;

Lallemand, P .

PHYSICS OF FLUIDS, 2001, 13 (11) :3452-3459

[6] STREAMLINE UPWIND PETROV-GALERKIN FORMULATIONS FOR CONVECTION DOMINATED FLOWS WITH PARTICULAR EMPHASIS ON THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [J].

BROOKS, AN ;

HUGHES, TJR .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1982, 32 (1-3) :199-259

[7] Prandtl number effects in MRT lattice Boltzmann models for shocked and unshocked compressible fluids [J].

Chen, Feng ;

Xu, Aiguo ;

Zhang, Guangcai ;

Li, Yingjun .

THEORETICAL AND APPLIED MECHANICS LETTERS, 2011, 1 (05)

[8] Multiple-relaxation-time lattice Boltzmann model for compressible fluids [J].

Chen, Feng ;

Xu, Aiguo ;

Zhang, Guangcai ;

Li, Yingjun .

PHYSICS LETTERS A, 2011, 375 (21) :2129-2139

[9] Probabilistic Analysis of the Upwind Scheme for Transport Equations [J].

Delarue, Francois ;

Lagoutiere, Frederic .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 199 (01) :229-268

[10] Two routes from the Boltzmann equation to compressible flow of polyatomic gases [J].

Dellar, Paul J. .

PROGRESS IN COMPUTATIONAL FLUID DYNAMICS, 2008, 8 (1-4) :84-96

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