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Kinetic Schemes for Saint-Venant Equations with Source Terms on Unstructured Grids

Authors
  • Audusse, Emmanuel
  • Bristeau, Marie-Odile
  • Perthame, Benoît
Publication Date
Jan 01, 2000
Source
HAL
Keywords
Language
English
License
Unknown
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Abstract

We consider the Saint-Venant (or Shallow Water) system which is an usual model to describe the flows in rivers or coastal areas. This hyperbolic system of conservation laws is solved on unstructured meshes by a kinetic scheme based on a finite volume approach. An important property of this scheme is the preservation of the water height positivity when applications with dry areas are considered. Following some hypothesis an entropy inequality is proved. The standard kinetic scheme is modified to deal with varying bed slope and particularly to preserve equilibrium states such as still water. Moreover the source terms due to the arbitrary bottom topography have to be discretized in such a way to balance the flux gradients for these equilibriums. We illustrate the properties of the scheme on different test cases for which exact solutions are available and on more realistic applications.

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