A new solution approach to the Serre equations

Abstract 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 analytica...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 86; no. 1; pp. 30 - 57
Main Author Jang, T S
Format Journal Article
LanguageEnglish
Published Oxford University Press 01.02.2021
Subjects
computational methods
amplitude solitary wave
Serre equations
solution procedure
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Summary:Abstract 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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxaa037