On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas

Authors:
José M. Gallardo;Carlos Parés;Manuel Castro
Affiliations:
Department of Mathematical Analysis, University of Málaga, Campus Teatinos s/n, 29080 Málaga, Spain;Department of Mathematical Analysis, University of Málaga, Campus Teatinos s/n, 29080 Málaga, Spain;Department of Mathematical Analysis, University of Málaga, Campus Teatinos s/n, 29080 Málaga, Spain
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

We present a finite volume scheme for solving shallow water equations with source term due to the bottom topography. The scheme has the following properties: it is high-order accurate in smooth wet regions, it correctly solves situations where dry areas are present, and it is well-balanced. The scheme is developed within a general nonconservative framework, and it is based on hyperbolic reconstructions of states. The treatment of wet/dry fronts is carried out by solving specific nonlinear Riemann problems at the corresponding intercells.