On step approximation for Roseau's analytical solution of water waves
type: Item
instance of: scholarly article
title: On step approximation for Roseau's analytical solution of water waves
zbMATH Open document ID: 1213.65145
DOI: 10.1155/2011/607196
author: C. C. Tsai
author: Tai-Wen Hsu
author: Yueh-Ting Lin
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/224563
review text: Summary: An indirect eigenfunction marching method (IEMM) is developed to provide step approximations for water wave problems. The bottom profile is in terms of successive flat shelves separated by abrupt steps. The marching conditions are represented by the horizontal velocities at the steps in the solution procedure. The approximated wave field can be obtained by solving a system of linear equations with unknown coefficients which represents the horizontal velocities under a proper basis. It is also demonstrated that this solution method can be exactly reduced to the transfer-matrix method (TM method) for a specific setting. The combined scattering effects of a series of steps can be described by a single two-by-two transfer matrix for connecting the far-field behaviors of both sides for this method. The solutions obtained by the IEMM are basically exact for water wave problems considering step-like bottoms. Numerical simulations were performed to validate the present and commonly used methods. Furthermore, it also shows that the solutions obtained by the IEMM converge very well to Roseau's analytical solutions for both mild and steep curved bottom profiles. The present method improves the converges of the TM method for solving water wave scattering over steep bathymetry.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 5904904
Wikidata QID: Q58693285
MaRDI profile type: Publication
OpenAlex ID: W1974887662
cites work: Q4086108
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description: scientific article; zbMATH DE number 5904904