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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: Manuel Castro, José M. Gallardo and Carlos Parés
Journal: Math. Comp. 75 (2006), 1103-1134
MSC (2000): Primary 65M06, 35L65; Secondary 76M12, 76B15
Published electronically: March 21, 2006
MathSciNet review: 2219021
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Abstract: 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.


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Additional Information

Manuel Castro
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071-Málaga, Spain
Email: castro@anamat.cie.uma.es

José M. Gallardo
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071-Málaga, Spain
Email: gallardo@anamat.cie.uma.es

Carlos Parés
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071-Málaga, Spain
Email: pares@anamat.cie.uma.es

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01851-5
PII: S 0025-5718(06)01851-5
Keywords: Hyperbolic systems, nonconservative products, well-balanced schemes, Roe methods, high order schemes, weighted ENO, shallow-water systems
Received by editor(s): November 30, 2004
Received by editor(s) in revised form: May 20, 2005
Published electronically: March 21, 2006
Additional Notes: This research has been partially supported by the Spanish Government Research project BFM2003-07530-C02-02
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.