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

TL;DR

This paper evaluates the relevance of nonlinear shallow water equations (NSWE) for flooding simulations by comparing them with detailed Navier-Stokes simulations, questioning their validity beyond classical dam break scenarios.

Contribution

It critically assesses the applicability of NSWE in flooding modeling, highlighting the assumptions and limitations of the mathematical model in real-world scenarios.

Findings

NSWE are valid under certain conditions for flooding simulations

Comparison shows discrepancies between NSWE and Navier-Stokes results

Future research directions for improving NSWE models are proposed

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.