Analytical approach of the transient Green's function solution for the linear three-dimensional wave-body interaction problem

This thesis considers the hydrodynamic solution of the linear wave interactions with a floating body at zero-speed conditions in a water body of infinite depth. The initial-boundary-value problem was linearized about the mean position of a body, and derived as a boundary integral equation for solving exterior velocity potential using Green's theorem and the impulsive Green's function in the time domain. In order to minimize time and errors in numerical evaluation, this thesis introduced the alternative solution of the time-domain free-surface Green's function based on the power series expansion method. The analytical forms in term of a power series were derived from the ordinary differential equation that were proven to be the solution of the original infinity integral of the time-domain free-surface Greens function. The purpose was to speed up the convergence of the summation of an infinite series in the numerical computation. Based on the analytical form developed, it was possible to perform procedures that speed up the evaluation of convolution integral involved in the boundary integral equation. Moreover, the singularity integral of the Rankine source was regularized and a numerical scheme using global discretization technique for regularized boundary integral equation with Gaussian quadrature was proposed. Analytical surface as well as Non-Uniform Rational B-Splines (NURBS) surfaces were employed to represent the body surface mathematically. Computed impulse response function and hydrodynamic coefficients due to radiated waves for a floating sphere and ellipsoid were compared with published results. The comparison was reasonable for all cases.