Numerical Time Integration Methods for a Point Absorber Wave Energy Converter

The objective of this abstract is to provide a review of models for motion simulation of marine structures with a special emphasis on wave energy converters. The time-domain model is applied to a point absorber system working in pitch mode only. The device is similar to the well-known Wavestar float located in the Danish North Sea. The main objective is to produce a tool that can accurately simulate the dynamics of a floating structure with an arbitrary geometry provided the frequency domain coefficients are calculated beforehand. The latter calculation is based on linear fluid structure interaction (small deformations of the fluid surface and body), inviscid incompressible, irrotational flow and a linearized Euler-Bernoulli formulation of the fluid pressure. The time-domain analysis of a floating structure involves the calculation of a convolution integral between the impulse response function of the radiation force and the unknown body velocity due to an external force. The convolution integral can be seen as a memory effect where the system response in the past affects the response in the future. Two different time-domain models will be presented. The first one is based on a discretization of the convolution integral. The calculation of the convolution integral is performed at each time step regardless of the chosen numerical scheme. In the second model the convolution integral is replaced by a system of linear ordinary differential equations. The formulation of the state-space model is advantageous regarding the computational effort and the robustness of the solver. Another important feature is the linear-time invariance of the system. In a next step the influence of the nonlinear hydrostatic behavior of the float is investigated by using a simplified formulation.