Time-domain simulations for floating structures

In this thesis numerical and analytical investigations of wave-structure interactions are conducted within the linearised theory of water waves. The primary objective of the thesis was to develop a numerical time-domain solution method capable of simulating wave-structure interactions in three-dimensions involving axisymmetric structures. Although the solution method was developed for three-dimensional problems, many two-dimensional interactions were also simulated using an existing time-domain solution method. The numerical method for obtaining the solution of the time-domain water wave problem combines a cubic spline boundary element method (BEM) which yields a solution to the boundary integral equation with a time-stepping algorithm to advance the solution in time. The assumption regarding the axisymmetric nature of the structural geometry results in significant simplifications of the governing boundary integral equation and allows the existing BEM implementation for two-dimensional problems to be used as the basis for the solution method. The time-advancement algorithm was implemented such that radiation, scattering and floating body interactions can be simulated. Despite the focus on the time-domain investigations, the interactions were also considered in the frequency-domain to complement the time-domain results and for the purposes of verification. The analytical frequency-domain investigations are particularly relevant to highly resonant interactions where the response of the fluid and structure is related to the location of the resonance in the complex frequency plane. The complementary frequency-domain analysis was utilised in the development of a damped harmonic oscillator model to approximate the transient fluid motions in resonant scattering interactions. Passive trapped modes which can be supported by both fixed and floating structures were discovered in frequency-domain uniqueness investigations in the water-wave problem for a floating structure and their existence was confirmed in both two and three dimensions using time-domain excitation simulations. Finally, the time-domain BEM code was utilised to simulate various wave-structure interactions of practical interest.