ABSTRACT

A simple and efficient method for computing the Green function (and its gradient) associated with the diffraction and the radiation of regular (time-harmonic) water waves by fixed offshore structures and moored floating offshore platforms in deep water is presented. The method is based on a representation of the Green function (and its gradient) as the sum of three terms:

  • an elementary (Rankine) source and a corresponding elementary free-surface mirror-image source,

  • a wave term which is everywhere continuous (in fact infinitely differentiable) and is given by the product of elementary functions of one variable, and

  • a more complex nonoscillatory near-field term which is singular and is a function of two variables.

The latter term is expressed as the sum of an elementary function that completely accounts for the singularity, and a remainder that is everywhere continuous and vanishes both at the singular point and at infinity. This term is evaluated in a simple and efficient way using linear table interpolation in a transformed function and coordinate space.

INTRODUCTION

Diffraction and radiation of regular (time-harmonic) water waves by fixed offshore structures and moored floating offshore platforms must be considered for determining linear and nonlinear wave loads and eventual related body motions and fluid-structure interactions, and thus is an important basic subject in offshore mechanics. Most existing numerical methods for predicting water-wave diffraction and radiation are based on integral equations and utilize the Green function associated with the linearized free-surface boundary condition for time-harmonic flows. Efficient methods for numerically evaluating this Green function and its gradient thus are essential, especially for the calculation of second-order hydrodynamic effects. Alternative methods have been developed by Newman (1985) and Telste and Noblesse (1986). These methods are based on polynomial approximations and analytically.

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