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Wave kinematic fields from the boundary integral method
Author(s) -
Sobey Rodney J.
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.1158
Subject(s) - boundary (topology) , mathematics , kinematics , mathematical analysis , integral equation , boundary element method , interpolation (computer graphics) , singular boundary method , domain (mathematical analysis) , ordinary differential equation , geometry , classical mechanics , physics , differential equation , finite element method , motion (physics) , thermodynamics
The predictive potential of interior domain solutions from the boundary integral method for 2D extreme wave kinematics is explored. Comparisons with analytical solutions for near‐limit waves confirms the susceptibility of the boundary integral method to poor precision at near‐boundary locations. Additionally, these comparisons identify a domain‐wide precision challenge that is associated with the relatively rapid changes in water surface geometry and kinematics that are typical of extreme waves. A numerical evaluation of Green's integral around the boundary addresses these precision issues through formulation of the integration as a simultaneous system of ordinary differential equations at a cubic level of approximation. Careful attention is given to consistent interpolation of all contributions to the Green's integral. Copyright © 2005 John Wiley & Sons, Ltd.