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Well-Balanced High-Order MUSTA Schemes for Non-Conservative Hyperbolic Systems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. J. Castro

    (U. de Málaga, Depto. de Análisis mátematico)

  • C. Parés

    (U. de Málaga, Depto. de Análisis mátematico)

  • A. Pardo

    (U. de Málaga, Depto. de Análisis mátematico)

  • E. F. Toro

    (University of Trento, Laboratory of Applied Mathematics. Faculty of Engineering)

Abstract

We introduce a Multi-Stage (MUSTA) approach for constructing upwind numerical schemes for nonconservative hyperbolic systems. MUSTA schemes for hyperbolic conservation laws were introduced in [8] as an approximate Riemann solver based on a GFORCE scheme and a predictor-corrector procedure. In [2] a path-conservative GFORCE numerical scheme (in the sense introduced in [6]) for nonconservative hyperbolic systems is proposed. Here, we propose a predictor-corrector procedure based on this extension of GFORCE to obtain a generalization of MUSTA schemes. These schemes can be applied to systems of conservation laws with source terms and nonconservative products. In particular, some applications to two-layer shallow-water flows are presented.

Suggested Citation

  • M. J. Castro & C. Parés & A. Pardo & E. F. Toro, 2008. "Well-Balanced High-Order MUSTA Schemes for Non-Conservative Hyperbolic Systems," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 249-256, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_29
    DOI: 10.1007/978-3-540-69777-0_29
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