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Mesh effects on the computation of small amplitude water waves
Author(s) -
Toro E. F.,
O'Carroll M. J.
Publication year - 1985
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.1650050602
Subject(s) - amplitude , crest , wavelength , computation , limiting , polygon mesh , mathematics , physics , mathematical analysis , flow (mathematics) , mechanics , classical mechanics , geometry , optics , algorithm , engineering , mechanical engineering
Computational difficulties arise in the non‐linear free‐surface problem for water waves both at large amplitudes when the crest becomes nearly singular and at small amplitudes when the wave is very close to the alternative uniform flow solution. Since the limiting wavelengths for small amplitude waves are known from the Stokes linearized theory, these are used in checking results for finite‐amplitude programs. When Southwell and Vaisey 1 first tried this, their methods gave an unexplained overestimate, by 6 per cent, of the limiting wavelength. This paper shows how coarse mesh effects can create such an overestimate, gives very accurate solutions at small amplitudes and considers accuracy in relation to the mesh for short and long waves.