On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas |
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Institution: | 1. CEN – Center for Earth System Research and Sustainability, Universität Hamburg, Grindelberg 5, Hamburg 20144, Germany;2. Department of Mathematics, Universität Hamburg, Bundesstraße 55, Hamburg 20146, Germany |
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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. |
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