THE RELAXATION SCHEMES FOR SYSTEMS OF CONSERVATION-LAWS IN ARBITRARY SPACE DIMENSIONS

被引:717
作者
JIN, S [1 ]
XIN, ZP [1 ]
机构
[1] NYU, COURANT INST MATH SCI, NEW YORK, NY 10012 USA
关键词
D O I
10.1002/cpa.3160480303
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with a small dissipative correction. The new system can be served by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally. Numerical results for 1-D and 2-D problems are presented. The second-order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations. (C) 1995 John Wiley & Sons, Inc.
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页码:235 / 276
页数:42
相关论文
共 28 条
[1]  
CAFLISCH R, UNPUB SIAM J NUMER A
[2]  
Chapman S., 1970, MATH THEORY NONUNIFO
[3]   HYPERBOLIC CONSERVATION-LAWS WITH STIFF RELAXATION TERMS AND ENTROPY [J].
CHEN, GQ ;
LEVERMORE, CD ;
LIU, TP .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1994, 47 (06) :787-830
[4]   LATTICE GAS MODELS FOR NONIDEAL GAS FLUIDS [J].
CHEN, SY ;
CHEN, HD ;
DOOLEN, GD ;
LEE, YC ;
ROSE, H ;
BRAND, H .
PHYSICA D, 1991, 47 (1-2) :97-111
[5]   MULTIDIMENSIONAL UPWIND METHODS FOR HYPERBOLIC CONSERVATION-LAWS [J].
COLELLA, P .
JOURNAL OF COMPUTATIONAL PHYSICS, 1990, 87 (01) :171-200
[6]   THE METHOD OF FRACTIONAL STEPS FOR CONSERVATION-LAWS [J].
CRANDALL, M ;
MAJDA, A .
NUMERISCHE MATHEMATIK, 1980, 34 (03) :285-314
[7]  
DESHPANDE SM, 1986, NASA2613 TECH PAP
[8]   SYSTEMS OF CONSERVATION EQUATIONS WITH A CONVEX EXTENSION [J].
FRIEDRICHS, KO ;
LAX, PD .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1971, 68 (08) :1686-+
[9]   A KINETIC CONSTRUCTION OF GLOBAL-SOLUTIONS OF 1ST ORDER QUASILINEAR EQUATIONS [J].
GIGA, Y ;
MIYAKAWA, T .
DUKE MATHEMATICAL JOURNAL, 1983, 50 (02) :505-515
[10]   ON THE ACCURACY OF STABLE SCHEMES FOR 2D SCALAR CONSERVATION-LAWS [J].
GOODMAN, JB ;
LEVEQUE, RJ .
MATHEMATICS OF COMPUTATION, 1985, 45 (171) :15-21