关于溃坝问题在非线性浅水方程背景下的相关性
On the relevance of the dam break problem in the context of nonlinear shallow water equations
AI总结：
通过两流体Navier-Stokes模拟与解析/数值求解的非线性浅水方程对比，检验NSWE在洪水模拟中的有效性，指出其数学推导要求总水深为正的限制。
摘要：
经典的溃坝问题已成为验证非线性浅水方程（NSWE）求解器的事实标准。此外，NSWE被广泛用于洪水模拟。虽然应用数学界主要专注于开发新的数值方案，但我们试图检验所考虑的数学模型的正确性。本研究的主要目的是检查NSWE在洪水过程中的适用性。从数学角度来看，答案并不明显，因为所有推导过程都假设总水深为正。我们进行了两流体Navier-Stokes模拟与解析和数值求解的NSWE之间的比较。得出了若干结论，并概述了未来研究的展望。
英文摘要：
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.
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