Numerical Study of the Ship Motion in Waves Using the Three-Dimensional Time-Domain Forward-Speed Free-Surface Green Function and a Second-Order Boundary Element Method

Abstract

The radiation and diffraction potentials of a ship advancing in waves are calculated in the time-domain using the three-dimensional time-domain forward-speed free-surface Green function and the Green integral equation on the basis of the Neumann-Kelvin linear wave hypothesis. The Green function approximated by Newman for large time is used together with the Green function by Lamb for small time. The time-domain diffraction problem is solved for the time derivative of the potential by using the time derivative of the impulsive incident wave potential represented by using the complementary complex error function. The integral equation for the potential is discretized according to a second-order boundary element method where the collocation points are located inside the panel. It makes it possible to take account of the line integral along the waterline in a rigorous manner. The six-degree-of-freedom motion and memory functions as well as the diffraction impulse response functions of a hemisphere and the Wigley seakeeping model are presented for various Froude numbers. Comparisons of the wave damping and exciting force and moment coefficients for zero forward speed, calculated by using the Fourier transforms of the time-domain results and the frequency-domain coefficients calculated by using the improved Green integral equation which is free of the irregular frequencies, have been shown to be satisfactory. The wave damping coefficients for non-zero forward speed, calculated by using Fourier transforming of the present time-domain results have also been compared to the experimental results and agreement between them has been shown to be good. A simulation of coupled heave-pitch motion of the Wigley seakeeping model advancing in regular head waves of unit amplitude has been carried out.