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

Denys Dutykh (1) , Dimitrios Mitsotakis (2)

1 LAMA - Laboratoire de Mathématiques
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: free surface flow; two-phase flow; shallow water equations; dam break problem; finite volume method

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Hydrologie; Milieux et Changements globaux; Océanographie; Milieux fluides et réactifs; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Analyse numérique [math.NA]; Physique Numérique [physics.comp-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Atmosphérique et Océanique [physics.ao-ph]; Océan, Atmosphère

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 - Series B, 2010, 13 (4), pp.799-818. ⟨10.3934/dcdsb.2010.13.799⟩. ⟨hal-00369795v4⟩