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

Abstract

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.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2010relevancebreak,
  author = {Dutykh, D. and Mitsotakis, D.},
  title = {On the relevance of the dam break problem in the context of nonlinear shallow water equations},
  journal = {Discrete and Continuous Dynamical Systems},
  year = {2010},
  volume = {13},
  number = {4},
  pages = {799--818},
  doi = {10.3934/dcdsb.2010.13.799},
  abstract = {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.},
  keywords = {dam break problem, applied mathematics, free surface flow, flooding simulations, numerical solutions, numerical schemes, mathematical model, analytical solutions, shallow water equations, finite volume method, two-phase flow, nonlinear shallow water equations, water depth, two-fluid Navier-Stokes simulations}
}