An explicit residual based approach for shallow water flows

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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Source https://inria.hal.science/hal-00855645
Author Ricchiuto, Mario
Maintainer CCSD
Last Updated May 9, 2026, 23:04 (UTC)
Created May 9, 2026, 23:04 (UTC)
Identifier Report N°: RR-8350
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems (BACCHUS) ; Centre Inria de l'Université de Bordeaux ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)
creator Ricchiuto, Mario
date 2013-08-29T00:00:00
harvest_object_id 8c78ad65-2521-411a-8a17-5c270f70f0c8
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-03-18T00:00:00
set_spec type:REPORT