High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

被引：76

作者：

Castro, M. J. ^{[1
]}

Fernandez-Nieto, E. D. ^{[2
]}

Ferreiro, A. M. ^{[3
]}

Garcia-Rodriguez, J. A. ^{[3
]}

Pares, C. ^{[1
]}

机构：

[1] Univ Malaga, Dpto Anal Matemat, Malaga 29080, Spain

[2] Univ Seville, Dpto Matemat Aplicada 1, E-41012 Seville, Spain

[3] Univ A Coruna, Dpto Matemat, La Coruna 15071, Spain

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2009年 / 39卷 / 01期

关键词：

Generalized Roe schemes; 2d Nonconservative hyperbolic systems; Nonconservative products; Finite volume schemes; Conservation laws; Source terms; Shallow water systems; Two-layer problems; Geophysical flows; FINITE-VOLUME SCHEMES; SHALLOW-WATER SYSTEMS; WELL-BALANCED SCHEME; CONSERVATION-LAWS; SOURCE TERMS; EQUATIONS; PRODUCTS; RECONSTRUCTION; PROPERTY; FLUXES;

D O I：

10.1007/s10915-008-9250-4

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 well-balanced high order Roe methods for two-dimensional nonconservative hyperbolic systems. In particular, we are interested in extending the methods introduced in (Castro et al., Math. Comput. 75:1103-1134, 2006) to the two-dimensional case. We also investigate the well-balance properties and the consistency of the resulting schemes. We focus in applications to one and two layer shallow water systems.

引用

页码：67 / 114

页数：48

共 32 条

[1] [Anonymous], 1967, Mat. Sb, V73, P255
[2] [Anonymous], 1989, 593 I MATH ITS APPL
[3] MAXIMAL 2-LAYER EXCHANGE THROUGH A CONTRACTION WITH BAROTROPIC NET FLOW
ARMI, L
FARMER, DM
[J]. JOURNAL OF FLUID MECHANICS, 1986, 164 : 27 - 51
[4] UPWIND METHODS FOR HYPERBOLIC CONSERVATION-LAWS WITH SOURCE TERMS
BERMUDEZ, A
VAZQUEZ, E
[J]. COMPUTERS & FLUIDS, 1994, 23 (08) : 1049 - 1071
[5] High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products.: Applications to shallow-water systems
Castro, Manuel
Gallardo, Jose E. M.
Pares, Carlos
[J]. MATHEMATICS OF COMPUTATION, 2006, 75 (255) : 1103 - 1134
[6] Why many theories of shock waves are necessary:: Convergence error in formally path-consistent schemes
Castro, Manuel J.
LeFloch, Philippe G.
Munoz-Ruiz, Maria Luz
Pares, Carlos
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 227 (17) : 8107 - 8129
[7] The numerical treatment of wet/dry fronts in shallow flows:: Application to one-layer and two-layer systems
Castro, MJ
Ferreiro, AMF
García-Rodríguez, JA
González-Vida, JM
Macías, J
Parés, C
Vázquez-Cendón, ME
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2005, 42 (3-4) : 419 - 439
[8] CASTRO MJ, 2008, COEFFICIENT SP UNPUB
[9] DalMaso G, 1995, J MATH PURE APPL, V74, P483
[10] Godlewski E., 1996, APPL MATH SCI, V118

← 1 2 3 4 →