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AN EXTENDED BOUNDARY INTEGRAL EQUATION METHOD FOR THE REMOVAL OF IRREGULAR FREQUENCY EFFECTS
Author(s) -
LEE C.H.,
NEWMAN J. N.,
ZHU X.
Publication year - 1996
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/(sici)1097-0363(19961015)23:7<637::aid-fld437>3.0.co;2-3
Subject(s) - velocity potential , integral equation , mathematical analysis , boundary value problem , boundary element method , mathematics , free surface , potential flow , potential theory , singularity , added mass , computation , mechanics , classical mechanics , physics , finite element method , vibration , acoustics , algorithm , thermodynamics
Numerical techniques for the analysis of wave–body interactions are developed by the combined use of two boundary integral equation formulations. The velocity potential, which is expressed in a perturbation expansion, is obtained directly from the application of Green's theorem (the ‘potential formulation’), while the fluid velocity is obtained from the gradient of the alternative form where the potential is represented by a source distribution (the ‘source formulation’). In both formulations, the integral equations are modified to remove the effect of the irregular frequencies. It is well known from earlier works that if the normal velocity is prescribed on the interior free surface, inside the body, an extended boundary integral equation can be derived which is free of the irregular frequency effects. It is shown here that the value of the normal velocity on the interior free surface must be continuous with that outside the body, to avoid a logarithmic singularity in the source strength at the waterline. Thus the analysis must be carried out sequentially in order to evaluate the fluid velocity correctly: first for the velocity potential and then for the source strength. Computations are made to demonstrate the effectiveness of the extended boundary integral euations in the potential and source formulations. Results are shown which include the added‐mass and damping coefficients and the first‐order wave‐exciting forces for simple three‐dimensional bodies and the second‐order forces on a tension‐leg‐platform. The latter example illustrates the importance of removing irregular frequency effects in the context of second‐order wave loads.