The wave energy sector has made and is still doing a great effort in order to open up a niche in the energy market, working on several and diverse concepts and making advances in all aspects towards more efficient technologies. However, economic viability has not been achieved yet, for which maximisation of power production over the full range of sea conditions is crucial. Precise mathematical models are essential to accurately reproduce the behaviour, including nonlinear dynamics, and understand the performance of wave energy converters. Therefore, nonlinear models must be considered, which are required for power absorption assessment, simulation of devices motion and model-based control systems. Main sources of nonlinear dynamics within the entire chain of a wave energy converter-incoming wave trains, wave-structure interaction, power takeoff systems or mooring lines-are identified, with especial attention to the wave-device hydrodynamic interaction, and their influence is studied in the present paper for different types of converters. In addition, different approaches to model nonlinear wave-device interaction are presented, highlighting their advantages and drawbacks. Besides the traditional Navier-Stokes equations or potential flow methods, 'new' methods such as system-identification models, smoothed particle hydrodynamics or nonlinear potential flow methods are analysed.

Most wave energy converters (WECs) are described by linear mathematical models, based on the main assumption of small amplitudes of motion. Notwithstanding the computational convenience, linear models can become inaccurate when large motions occur. On the other hand, nonlinear models are often time consuming to simulate, while model-based controllers require system dynamic models which can execute in real time. Therefore, this paper proposes a computationally efficient representation of nonlinear static and dynamic Froude-Krylov forces, valid for any heaving axisymmetric point absorber. Nonlinearities are increased by nonuniform WEC cross sectional area and large displacements induced by energy maximising control strategies, which prevent the device from behaving as a wave follower. Results also show that the power production assessment realized through a linear model can be overly optimistic and control parameters calculations should also reflect the true nonlinear nature of the WEC model.

Designing, optimizing and controlling a wave energy converter requires the construction of a mathematical model in order to simulate the behaviour of the device. Given the nonlinear nature of fluid-structure interactions, the definition of the model is not straightforward and should take into account the specific application it is intended for. Two of the most important characteristics of a model are the computational time and the expected accuracy, which usually are mutually conflicting. The inclusion of nonlinearities potentially increases the model accuracy, but at a higher computational price. Considering a heaving wave energy converter with and without the application of latching control, this paper studies and compares nine different modelling options, eight of which are based on potential theory and consider nonlinear Froude-Krylov and viscous drag forces, while one is based on fully-nonlinear computational fluid dynamics. The value of including nonlinearities in the hydrodynamic model is discussed in relation to the computational cost of the eventual accuracy benefits, under a range of scenarios.

Results from the Collaborative Computational Project in Wave Structure Interaction (CCP-WSI) Blind Test Series 3 are presented. Participants, with numerical methods, ranging from low-fidelity linear models to high-fidelity Navier-Stokes (NS) solvers, simulate the interaction between focused waves and floating structures without prior access to the physical data. The waves are crest-focused NewWaves with various crest heights. Two structures are considered: a hemispherical-bottomed buoy and a truncated cylinder with a moon-pool; both are taut-moored with one linear spring mooring. To assess the predictive capability of each method, numerical results for heave, surge, pitch and mooring load are compared against corresponding physical data. In general, the NS solvers appear to predict the behaviour of the structures better than the linearised methods but there is considerable variation in the results (even between similar methods). Recommendations are made for future comparative studies and development of numerical modelling standards.

Two of the most common modes of oscillation of single degree of freedom wave energy converters are heave and surge, which are, respectively, exploited by heaving point absorbers (HPAs), and oscillating wave surge converters (OWSCs). Given major hydrodynamic differences between HPAs and OWSC, different nonlinear forces may be more or less relevant. Likewise, the scaling properties of such nonlinear forces may be different, according to the type of device, introducing uncertainties. This paper studies different nonlinear effects, and the relevance of different hydrodynamic force components, in HPAs and OWSCs. Nonlinear Froude-Krylov forces, as well as viscous drag effects, are represented and both prototype and full-scale device sizing are considered. Results show that HPAs are predominantly affected by nonlinear Froude-Krylov forces, while the most important hydrodynamic forces in OWSCs are diffraction and radiation effects. In addition, viscous drag appears to have little relevance in HPAs, but a significant influence in OWSCs. Finally, nonlinearities are shown to significantly affect the phase of the different force components.

In order to increase the overall power production efficiency of wave energy technology in the face of sea state variability, the presence of the control is mandatory. A model of the system is required to tune the controller parameters and predict the resulting performances. Even though the relevance of nonlinearities is magnified by the presence of the controller, the device model employed is usually linear. An implementation of control in a fully nonlinear simulation model is desirable, but missing. Hence, this paper proposes to use the fully nonlinear computational fluid dynamics (CFD) environment, implementing the latching control strategy in the open source software OpenFOAM. A case study has been analyzed to highlight the nonlinear behavior of a device under latching control and to evaluate the differences between linear and nonlinear simulation models. The results show that the linear model overestimates the amplitude of motion, and, as a result, the extracted power. Moreover, the choice of the optimal control parameter is significantly affected by the nonlinear effect on the natural period of the device.

High accuracy at a low computational time is likely to be a fundamental trait for mathematical models for wave energy converters, in order to be effective tools for reliable motion prediction and power production assessment, device and controller design, and loads estimation. Wave energy converters are particularly prone to exhibit complex and nonlinear behaviours, which are difficult to be modelled efficiently. Highlynonlinear effects, related to nonlinear Froude-Krylov forces, are nonlinear coupling, instability, and parametric resonance, which may damage or improve the power production. It is therefore fundamental to be able to describe such nonlinearities, in order to assess their repercussion on the performance of the device, and eventually design the system in order to exploit them. This paper provides a computationally efficient, compact, and flexible modelling approach for describing nonlinear Froude-Krylov forces for axisymmetric wave energy devices, in 6 degrees of freedom. Unlike other similar models, based on a mesh discretization of the geometry, the analytical formulation of the wetted surface allows the dynamical model to run almost in real time.

Although it is widely accepted that accurate modeling of wave energy converters is essential for effective and reliable design, it is often challenging to define an accurate model which is also fast enough to investigate the design space or to perform extensive sensitivity analysis. In fact, the required accuracy is usually brought by the inclusion of nonlinearities, which are often time-consuming to compute. This paper provides a computationally efficient meshless nonlinear Froude–Krylov model, including nonlinear kinematics and an integral formulation of drag forces in six degrees of freedom, which computes almost in real-time. Moreover, a mooring system model with three lines is included, with each line comprising of an anchor, a jumper, and a clump weight. The mathematical model is used to investigate the highly-nonlinear phenomenon of parametric resonance, which has particularly detrimental effects on the energy conversion performance of the spar-buoy oscillating water column (OWC) device. Furthermore, the sensitivity on changes to jumper and clump-weight masses are discussed. It is found that mean drift and peak loads increase with decreasing line pre-tension, eventually leading to a reduction of the operational region. On the other hand, the line pre-tension does not affect power production efficiency, nor is it able to avoid or significantly limit the severity of parametric instability.