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High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and Shallow Water Equations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. J. Castro

    (U. de Málaga, Dpto. de Análisis Matemático)

  • E. D. Fernández Nieto

    (U. de Sevilla, Dpto. Matemática Aplicada I)

  • A. M. Ferreiro Ferreiro

    (U. de A Coruña, Dpto. de Matemáticas)

  • J. A. García Rodríguez

    (U. de A Coruña, Dpto. de Matemáticas)

  • C. Parés

    (U. de Málaga, Dpto. de Análisis Matemático)

Abstract

In this article we apply a second order 2d scheme for non-conservative hyperbolic systems based on state reconstructions, for the modelization of the transport of a pollutant in a fluid. The mathematical model consists in the coupling of a system of shallow water system and a transport equation. That coupling gives rise to a new linearly degenerated field in the system. Therefore, to approximate the evolution of the pollutant, it is necessary to consider numerical methods that can capture accurately those contact discontinuities.

Suggested Citation

  • M. J. Castro & E. D. Fernández Nieto & A. M. Ferreiro Ferreiro & J. A. García Rodríguez & C. Parés, 2008. "High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and Shallow Water Equations," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 241-248, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_28
    DOI: 10.1007/978-3-540-69777-0_28
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