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A 2d Well-balanced Positivity Preserving Second Order Scheme for Shallow Water Flows on Unstructured Meshes

Emmanuel Audusse 1 Marie-Odile Bristeau 1
1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : We consider the solution of the Saint-Venant equations with topographic source terms on 2D unstructured meshes by a finite volume approach. We first present a stable and positivity preserving homogeneous solver issued from a kinetic representation of this hyperbolic conservation laws system. This water depth positivity property is important when dealing with wet-dry interfaces. Then we introduce a local hydrostatic reconstruction that preserves the positivity properties of the homogeneous solver and leads to a well-balanced scheme satisfying the steady state condition of still water. Finally a second order extension based on limited reconstructed values on both sides of each interface and on an enriched interpretation of the source terms satisfies the same properties and gives a noticeable accuracy improvement. Numerical examples on academic and real problems are presented.
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https://hal.inria.fr/inria-00070738
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 9:28:45 PM
Last modification on : Wednesday, December 9, 2020 - 3:11:24 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:49:09 PM

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  • HAL Id : inria-00070738, version 1

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Emmanuel Audusse, Marie-Odile Bristeau. A 2d Well-balanced Positivity Preserving Second Order Scheme for Shallow Water Flows on Unstructured Meshes. [Research Report] RR-5260, INRIA. 2004, pp.31. ⟨inria-00070738⟩

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