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A parametric finite‐difference method for shallow sea waves
Author(s) -
Bratsos A. G.,
Famelis I. Th.,
Prospathopoulos A. M.
Publication year - 2006
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.1252
Subject(s) - parametric statistics , finite difference method , finite difference , generalization , mathematics , set (abstract data type) , amplitude , stability (learning theory) , mathematical analysis , calculus (dental) , computer science , physics , medicine , statistics , dentistry , machine learning , programming language , quantum mechanics
This paper presents a parametric finite‐difference scheme concerning the numerical solution of the one‐dimensional Boussinesq‐type set of equations, as they were introduced by Peregrine ( J. Fluid Mech. 1967; 27 (4)) in the case of waves relatively long with small amplitudes in water of varying depth. The proposed method, which can be considered as a generalization of the Crank‐Nickolson method, aims to investigate alternative approaches in order to improve the accuracy of analogous methods known from bibliography. The resulting linear finite‐difference scheme, which is analysed for stability using the Fourier method, has been applied successfully to a problem used by Beji and Battjes ( Coastal Eng. 1994; 23 : 1–16), giving numerical results which are in good agreement with the corresponding results given by MIKE 21 BW (User Guide. In: MIKE 21 , Wave Modelling , User Guide . 2002; 271–392) developed by DHI Software. Copyright © 2006 John Wiley & Sons, Ltd.