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A Hybrid Second Order Scheme for Shallow Water Flows

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Abstract

We extend the well-balanced second order hybrid scheme developed in Donat and Martinez-Gavara (J. Sci. Comput., to appear) to the one-dimensional and two-dimensional shallow water system. We show that the scheme is exactly well-balanced for quiescent steady states, when a particular integration formula is employed, just as in the scalar models considered in Donat and Martinez-Gavara (J. Sci. Comput., to appear). A standard treatment of wet/dry fronts can easily be adapted, obtaining a robust scheme that produces well-resolved numerical solutions.

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Authors and Affiliations

  1. Departamento de Ecuaciones Difererenciales y Análisis Numérico, Universidad de Sevilla, Avda. Reina Mercedes 2, 41012, Sevilla, Spain

    A. Martinez-Gavara

  2. Departament de Matematica Aplicada, Universitat de Valencia, Avd. Vicent Andrés Estellés s/n, 46100, Burjassot, Spain

    R. Donat

Authors
  1. A. Martinez-Gavara
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  2. R. Donat
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Correspondence to A. Martinez-Gavara.

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Martinez-Gavara, A., Donat, R. A Hybrid Second Order Scheme for Shallow Water Flows. J Sci Comput 48, 241–257 (2011). https://doi.org/10.1007/s10915-010-9440-8

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  • DOI: https://doi.org/10.1007/s10915-010-9440-8

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