A Saint Venant model for gravity driven shallow water flows with variable density and compressibility effects

  • Authors:

  • TomáS Morales De Luna

  • Affiliations:

  • Département de Mathématiques et Applications, ícole Normale Supérieure, 45 rue d'Ulm, 75230 Paris cedex 05, France

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2008

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Abstract

We introduce a new model for shallow water flows with non-flat bottom made of two layers of compressible-incompressible fluids. The classical Savage-Hutter model for gravity driven shallow water flows is derived from incompressible Euler equations. Here, we generalize this model by adding an upper compressible layer. We obtain a model of shallow water type, that admits an entropy dissipation inequality, preserves the steady state of a lake at rest and gives an approximation of the free surface compressible-incompressible Euler equations.