A Saint Venant model for gravity driven shallow water flows with variable density and compressibility effects. Morales de Luna, T. Paper abstract bibtex 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. Keywords: Shallow water; Variable density; Compressibility; Entropy inequality; Savage–Hutter model

@article{morales_de_luna_saint_2008,
title = {A Saint Venant model for gravity driven shallow water flows with variable density and compressibility effects},
url = {http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6V0V-4NTJH02-6&amp;_user=10&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_sort=d&amp;view=c&amp;_acct=C000050221&amp;_version=1&amp;_urlVersion=0&amp;_userid=10&amp;md5=c714fddce3783429707813d440feb62a},
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. Keywords: Shallow water; Variable density; Compressibility; Entropy inequality; Savage–Hutter model},
journaltitle = {Mathematical and Computer Modelling},
author = {Morales de Luna, Tomás},
date = {2008},
keywords = {Shallow water, Compressibility, Entropy inequality, Savage Hutter model, Variable density},
}

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