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June  2010, 13(4): 799-818. doi: 10.3934/dcdsb.2010.13.799

On the relevance of the dam break problem in the context of nonlinear shallow water equations

Denys Dutykh 1, and  Dimitrios Mitsotakis 2,

1. 

Université de Savoie, CNRS-LAMA, Campus Scientifique, 73376 Le Bourget-du-Lac, France
2. 

UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, P.O. Box, 91405 Orsay, France

Received  March 2009 Revised  May 2009 Published  March 2010

The classical dam break problem has become the de factostandard in validating the nonlinear shallow water equations solvers. Moreover, the NSWE are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration. The main purpose of this study is to check the pertinence of the NSWE for flooding processes. From the mathematical point of view, the answer is not obvious since all derivation procedures assumes the total water depth positivity. We performed a comparison between the two-fluid Navier-Stokes simulations and the NSWE solved analytically and numerically. Several conclusions are drawn out and perspectives for future research are outlined.
Keywords: shallow water equations, Free surface flow, dam break problem, two-phase flow, finite volume method..
Mathematics Subject Classification: Primary: 76B15, 76T10; Secondary: 74S1.
Citation: Denys Dutykh, Dimitrios Mitsotakis. On the relevance of the dam break problem in the context of nonlinear shallow water equations. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 799-818. doi: 10.3934/dcdsb.2010.13.799
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