Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 799 - 818, Volume 13, Issue 4, June 2010      doi:10.3934/dcdsb.2010.13.799

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Denys Dutykh - Université de Savoie, CNRS-LAMA, Campus Scientifique, 73376 Le Bourget-du-Lac, France (email)
Dimitrios Mitsotakis - UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, P.O. Box, 91405 Orsay, France (email)

Abstract: 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:  Free surface flow, two-phase flow, shallow water equations, dam break problem, finite volume method.
Mathematics Subject Classification:  Primary: 76B15, 76T10; Secondary: 74S10.

Received: March 2009;      Revised: May 2009;      Available Online: March 2010.