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A spectral boundary integral method for inviscid water waves in a finite domain
Author(s) -
Im JeongSook,
Billingham John
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4225
Subject(s) - inviscid flow , spurious relationship , spectral method , mathematics , representation (politics) , boundary (topology) , chebyshev filter , mathematical analysis , domain (mathematical analysis) , chebyshev polynomials , boundary value problem , geometry , mechanics , physics , statistics , politics , political science , law
Summary In this paper, we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls, and also how it can be modified to take into account water of finite depth with a spatially varying bottom. In each case, we use Chebyshev polynomials as the basis of our representation of the solution and filtering to remove spurious high‐frequency modes. We show that spectral accuracy can be achieved until wave breaking, plunging or wall impingment occurs in two model problems. Copyright © 2016 John Wiley & Sons, Ltd.