A Hybrid Second Order Scheme for Shallow Water Flows

Authors:
A. Martinez-Gavara;R. Donat
Affiliations:
Departamento de Ecuaciones Difererenciales y Análisis Numérico, Universidad de Sevilla, Sevilla, Spain 41012;Departament de Matematica Aplicada, Universitat de Valencia, Burjassot, Spain 46100
Venue:
Journal of Scientific Computing
Year:
2011

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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.