A two‐dimensional numerical scheme of dry/wet fronts for the Saint‐Venant system of shallow water equations |
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Authors: | Zsolt Horváth Jürgen Waser Rui A. P. Perdigão Artem Konev Günter Blöschl |
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Affiliation: | 1. Institute of Hydraulic Engineering and Water Resources Management, Vienna University of Technology, Karlsplatz 13/222, 1040 Vienna, Austria;2. VRVis Zentrum für Virtual Reality und Visualisierung Forschungs‐GmbH, Donau‐City‐Strasse 1, 1220 Vienna, Austria;3. Centre for Water Resource Systems, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria |
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Abstract: | We propose a new two‐dimensional numerical scheme to solve the Saint‐Venant system of shallow water equations in the presence of partially flooded cells. Our method is well balanced, positivity preserving, and handles dry states. The latter is ensured by using the draining time step technique in the time integration process, which guarantees non‐negative water depths. Unlike previous schemes, our technique does not generate high velocities at the dry/wet boundaries, which are responsible for small time step sizes and slow simulation runs. We prove that the new scheme preserves ‘lake at rest’ steady states and guarantees the positivity of the computed fluid depth in the partially flooded cells. We test the new scheme, along with another recent scheme from the literature, against the analytical solution for a parabolic basin and show the improved simulation performance of the new scheme for two real‐world scenarios. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | shallow water finite volume hydrodynamics partial differential equations differential equations verification |
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