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Journal of Scientific Computing

, Volume 39, Issue 1, pp 67–114 | Cite as

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

  • M. J. CastroEmail author
  • E. D. Fernández-Nieto
  • A. M. Ferreiro
  • J. A. García-Rodríguez
  • C. Parés
Article

Abstract

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.

Keywords

Generalized Roe schemes 2d Nonconservative hyperbolic systems Nonconservative products Finite volume schemes Conservation laws Source terms Shallow water systems Two-layer problems Geophysical flows 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • M. J. Castro
    • 1
    Email author
  • E. D. Fernández-Nieto
    • 2
  • A. M. Ferreiro
    • 3
  • J. A. García-Rodríguez
    • 3
  • C. Parés
    • 1
  1. 1.Dpto. de Análisis MatemáticoUniversidad de MálagaMálagaSpain
  2. 2.Dpto. de Matemática Aplicada IUniversidad de SevillaSevillaSpain
  3. 3.Dpto. de MatemáticasUniversidad de A CoruñaA CoruñaSpain

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