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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
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by Manuel Castro, José M. Gallardo and Carlos Parés HTML | PDF
Math. Comp. 75 (2006), 1103-1134 Request permission

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
  • 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
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 75 (2006), 1103-1134
  • MSC (2000): Primary 65M06, 35L65; Secondary 76M12, 76B15
  • DOI: https://doi.org/10.1090/S0025-5718-06-01851-5
  • MathSciNet review: 2219021