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On the relevance of the dam break problem in the context of nonlinear shallow water equations
The classical dam break problem has become the de facto standard in
validating the Nonlinear Shallow Water Equations (NSWE) 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.Comment: 20 pages, 15 figures. Accepted to Discrete and Continuous Dynamical
Systems. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutyk
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