High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products.: Applications to shallow-water systems

被引：249

作者：

Castro, Manuel ^{[1
]}

Gallardo, Jose E. M. ^{[1
]}

Pares, Carlos ^{[1
]}

机构：

[1] Univ Malaga, Fac Ciencias, Dept Anal Matemat, E-29071 Malaga, Spain

来源：

MATHEMATICS OF COMPUTATION | 2006年 / 75卷 / 255期

关键词：

hyperbolic systems; nonconservative products; well-balanced schemes; Roe methods; high order schemes; weighted ENO; shallow-water systems;

D O I：

10.1090/S0025-5718-06-01851-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the development of high order methods for the numerical approximation of one-dimensional nonconservative hyperbolic systems. In particular, we are interested in high order extensions of the generalized Roe methods introduced by I. Toumi in 1992, based on WENO reconstruction of states. We also investigate the well-balanced properties of the resulting schemes. Finally, we will focus on applications to shallow-water systems.

引用

页码：1103 / 1134

页数：32

共 39 条

[1]

ANDRIANOV N, CONSTRUCT COLLECTION

[2]

[Anonymous], 1997, 9765 ICASE

[3] UPWIND METHODS FOR HYPERBOLIC CONSERVATION-LAWS WITH SOURCE TERMS [J].

BERMUDEZ, A ;

VAZQUEZ, E .

COMPUTERS & FLUIDS, 1994, 23 (08) :1049-1071

[4]

Bouchut F., 2004, Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes. Frontiers in Mathematics

[5]

CASELLES V, UNPUB FLUX GRADIENT

[6] A Q-scheme for a class of systems of coupled conservation laws with source term.: Application to a two-layer 1-D shallow water system [J].

Castro, M ;

Macías, J ;

Parés, C .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2001, 35 (01) :107-127

[7]

CHACON T, 2005, WELL BALANCED FINITE

[8]

CHACON T, 2003, ESAIM-MATH MODEL NUM, V37, P755

[9]

CHACON T, 2003, COMPUT METHODS APPL, V192, P203

[10]

CHINNAYA A, NEW GEN RIEMANN SOLV

← 1 2 3 4 →