Computational performance of a fast nonlinear Froude-Krylov force calculation approach for axisymmetric and prismatic floaters

Floating wave energy converters usually exhibit significant nonlinear behaviour, especially due to large variations of the wetted surface even during normal operation. In fact, in order to maximise energy extraction, the system is driven as far away from equilibrium as allowed by technical constraints. Consequently, the reliability of linear models is often doubted; however, although potentially inaccurate, linear models are widely adopted, thanks to their great computational convenience. In the wide family of nonlinear models, the ones based on nonlinear Froude-Krylov force calculations are attracting growing attention. Nevertheless, general mesh-based approaches are still about 2 orders of magnitude slower than real-time. In recent years, a computationally convenient formulation has been proposed for both axisymmetric and prismatic floaters, based on the analytical representation of the wetted surface. An open source demonstration toolbox is also available. The purpose of this paper is to present the mathematical framework and to provide a critical discussion of its computational performance, considering: two numerical integration algorithms; influence of absolute and relative tolerances; impact of integrand characteristics and perturbation to the rest position; importance of number of spectral components. Regardless, it is shown that each force evaluation takes about 1 ms, hence enabling computation much faster than real-time.