The study of wave induced loads and motions on structures is one of the fundamental problems for hydrodynamics. The solution of this problem is an economical requirement for the prediction of seakeeping ability of ships and the adaptation of design, to improve their performance. The harmonic Green's function with forward speed has been known for a long time, but the firrst attempts to obtain numerical results date back to the beginning of the eighties". Because of the complexity of this function, and of computer limitations, numerical results were quite difficult to obtain. To simplify the diffraction-radiation with forward speed codes, various authors have proposed reduced formulations by neglecting various terms in the free-surface boundary conditions. But to compute the unsteady flow around bodies close to the free-surface for any value of frequency and forward speed, it is necessary to have a fast and efficient method to compute the Green's function and its derivatives. Such a method, usable on a personal computer, is presented. This unsteady flow field due to the forward speed and oscillatory motions of a body moving with a constant horizontal velocity in waves is complicated by the interaction between the steady waves (Kelvin waves) and the unsteady waves (radiation waves). This interaction is studied for various magnitudes of the forward speed and the frequency of oscillation.
The general problem of the seakeeping of a floating structure or of a device moving through waves is relevant to several civil or military applications. Today, few solutions are proposed for the numerical resolution of this full problem of diffraction-radiation with forward speed in a three-dimensional flow. Various physical models to predict the seakeeping of structures can be developed, but they are limited for various reasons: -series of systematic tests are long and expensive due to the numerous parameters involved for a ship: Froude number; wave period, curvature and angle of incidence; depth of immersion of the fluid domain.