A Nonlinear Frequency-Domain Approach for Numerical Simulation of Wave Energy Converters

Nonlinear, analytical wave-energy converter (WEC) models are generally simulated through time-domain (TD) numerical integration. However, the relatively high computational requirements of TD integration are not compatible with applications where a large number of simulations are needed. Spectral domain (SD) linearization has also been proposed to take into account some nonlinear effects, while being much faster than TD integration. However, as explained in this paper, such SD models have limited accuracy, and cannot extend to the static nonlinear forces. In this paper, a nonlinear frequency-domain (NLFD) method is investigated for WEC simulation, using a projection of the dynamical equations onto a basis of trigonometric functions. A comparison with TD integration (second-order Runge$-$Kutta-RK2) and SD methods is provided, through theoretical considerations, and by means of numerical simulations based on two case studies. In the cases considered, the proposed NLFD method allows for significant computational savings compared to RK2 integration, without requiring any approximation for the radiation forces. NLFD thus shows promising potential for applications involving extensive WEC simulation, such as power production assessment, while preserving the WEC model accuracy. Although slower than SD, NLFD has significant benefits in terms of accuracy and range of applicability.