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Application of conservative residual distribution schemes to the solution of the shallow water equations on
 

Summary: Application of conservative residual distribution schemes
to the solution of the shallow water equations on
unstructured meshes
M. Ricchiuto a,*, R. Abgrall a,b
, H. Deconinck c
a
INRIA Futurs, Projet Scalapplix and Mathe´matiques Applique´es de Bordeaux, Universite´ Bordeaux 1,
351, Course de la Libe´ration, 33405 Talence Cedex, France
b
Institut Universitaire de France, Universite´ Bordeaux 1, 351, Course de la Libe´ration, 33405 Talence Cedex, France
c
von Karman Institute for Fluid Dynamics, 72, Chausse´e de Waterloo, B-1640 Rhode-St-Gene`se, Belgium
Received 3 November 2005; received in revised form 29 May 2006; accepted 8 June 2006
Available online 2 August 2006
Abstract
We consider the numerical solution of the shallow water equations on unstructured grids. We focus on flows over wet
areas. The extension to the case of dry bed will be reported elsewhere. The shallow water equations fall into the category of
systems of conservation laws which can be symmetrized thanks to the existence of a mathematical entropy coinciding, in
this case, with the total energy. Our aim is to show the application of a particular class of conservative residual distribution
ðRDÞ schemes to the discretization of the shallow water equations and to analyze their discrete accuracy and stability

  

Source: Abgrall, Rémi - Institut de Mathematiques de Bordeaux, Université Bordeaux

 

Collections: Mathematics