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A new solution approach to the Serre equations
IMA Journal of Applied Mathematics ( IF 1.2 ) Pub Date : 2020-10-12 , DOI: 10.1093/imamat/hxaa037
T S Jang 1
Affiliation  

This paper concerns constructing a semi-analytic solution procedure for integrating the fully non-linear Serre equations (or 1D Green–Naghdi equations for constant water depth). The validity of the solution procedure is checked by investigating a moving solitary wave for which the analytical solution is known. The semi-analytic procedure constructed in this study is confirmed to be good at observing non-linear wave phenomena of the collision of a sufficiently high-amplitude solitary wave with a vertical wall. The simulated results are in a good agreement with data of other authors. Further, the procedure simulates the non-linear interaction of four solitary waves, which enables us to investigate the repeated reflection of a single solitary wave between two vertical walls.

中文翻译:

Serre方程的新解法

本文涉及构造一个半解析解程序,以整合完全非线性的Serre方程(或恒定水深的一维Green-Naghdi方程)。通过研究已知的解析解的移动孤波来检验解法的有效性。经证实,本研究构建的半解析程序可以很好地观察非线性振幅孤波与垂直壁碰撞的非线性波动现象。模拟结果与其他作者的数据非常吻合。此外,该过程模拟了四个孤立波的非线性相互作用,这使我们能够研究重复的 两个垂直壁之间的单个孤立波的反射。
更新日期:2020-10-12
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