inria-00070738, version 1
A 2d Well-balanced Positivity Preserving Second Order Scheme for Shallow Water Flows on Unstructured Meshes
N° RR-5260 (2004)
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.
- 1:
- INRIA – Laboratoire Jacques-Louis Lions
- Domain : Computer Science/Other
- Keywords : SAINT-VENANT SYSTEM / SHALLOW WATER FLOW / HYPERBOLIC SYSTEMS / FINITE VOLUMES / KINETIC SOLVER / HYDROSTATIC RECONSTRUCTION / WELL-BALANCED SCHEME / POSITIVITY PRESERVING SCHEME / SECOND ORDER EXTENSION
- Internal note : RR-5260
- inria-00070738, version 1
- http://hal.inria.fr/inria-00070738
- oai:hal.inria.fr:inria-00070738
- From:
- Submitted on: Friday, 19 May 2006 21:28:45
- Updated on: Wednesday, 7 March 2007 12:45:47





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