Physics – Classical Physics
Scientific paper
2009-03-21
Discrete and Continuous Dynamical Systems - Series B 13, 4 (2010) 799-818
Physics
Classical Physics
20 pages, 15 figures. Accepted to Discrete and Continuous Dynamical Systems. Other author's papers can be downloaded at http
Scientific paper
10.3934/dcdsb.2010.13.799
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.
Dutykh Denys
Mitsotakis Dimitrios
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