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inria-00070738, version 1

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

Emmanuel Audusse 1, Marie-Odile Bristeau () 1

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:  BANG (INRIA Rocquencourt)
  • 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
  • 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