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An explicit residual based approach for shallow water flows

Mario Ricchiuto 1, 2 
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We describe a fully explicit residual based construction to discretize the shallow water equations with friction on unstructured grids. The approach is by construction exactly well balanced for al the simple known steady equilibria, and it shows a super-covergent behavior for smooth non-trivial equilibria, as the implicit residual schemes considered in (Ricchiuto, J.Sci.Comp. 48,2011). Moreover, by adapting the wetting drying technique discussed in (Ricchiuto and Bolermann, JCP 228, 2009) the scheme is able to preserve the non-negativity of the depth and to handle very well the runup and flooding of complex bathymetries. The approach is analyzed and tested thoroughly. The numerical results on a large variety of problems show the interest in the approach.
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https://hal.inria.fr/hal-00855645
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Submitted on : Thursday, August 29, 2013 - 4:47:35 PM
Last modification on : Thursday, January 20, 2022 - 5:31:40 PM
Long-term archiving on: : Thursday, April 6, 2017 - 10:36:42 AM

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Mario Ricchiuto. An explicit residual based approach for shallow water flows. [Research Report] RR-8350, INRIA. 2013. ⟨hal-00855645⟩

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