Mathematical analysis is an essential tool for the successful development and operation of wave energy converters (WECs). Mathematical models of moorings systems are therefore a requisite in the overall techno-economic design and operation of floating WECs. Mooring models (MMs) can be applied to a range of areas, such as WEC simulation, performance evaluation and optimisation, control design and implementation, extreme load calculation, mooring line fatigue life evaluation, mooring design, and array layout optimisation. The mathematical modelling of mooring systems is a venture from physics to numerics, and as such, there are a broad range of details to consider when applying MMs to WEC analysis. A large body of work exists on MMs, developed within other related ocean engineering fields, due to the common requirement of mooring floating bodies, such as vessels and offshore oil and gas platforms. This paper reviews the mathematical modelling of the mooring systems for WECs, detailing the relevant material developed in other offshore industries and presenting the published usage of MMs for WEC analysis.

This review focuses on the most suitable form of hydrodynamic modeling for the next generation wave energy converter (WEC) design tools. To design and optimize a WEC, it is estimated that several million hours of operation must be simulated, perhaps one million hours of WEC simulation per year of the R&D program. This level of coverage is possible with linear potential flow (LPF) models, but the fidelity of the physics included is not adequate. Conversely, while Reynolds averaged Navier–Stokes (RANS) type computational fluid dynamics (CFD) solvers provide a high fidelity representation of the physics, the increased computational burden of these models renders the required amount of simulations infeasible. To scope the fast, high fidelity options, the present literature review aims to focus on what CFD theories exist intermediate to LPF and RANS as well as other modeling options that are computationally fast while retaining higher fidelity than LPF.

A fully non-linear numerical wave tank (NWT), based on Computational Fluid Dynamics (CFD), provides a useful tool for the analysis of coastal and offshore engineering problems. To generate and absorb free surface waves within a NWT, a variety of numerical wave maker (NWM) methodologies have been suggested in the literature. Therefore, when setting up a CFD-based NWT, the user is faced with the task of selecting the most appropriate NWM, which should be driven by a rigorous assessment of the available methods. To provide a consistent framework for the quantitative assessment of different NWMs, this paper presents a suite of metrics and methodologies, considering three key performance parameters: accuracy, computational requirements and available features. An illustrative example is presented to exemplify the proposed evaluation metrics, applied to the main NWMs available for the open source CFD software, OpenFOAM. The considered NWMs are found to reproduce waves with an accuracy comparable to real wave makers in physical wave tank experiments. However, the paper shows that significant differences are found between the various NWMs, and no single method performed best in all aspects of the assessment across the different test cases.

Energy maximising controllers, for wave energy converters (WECs),based on linear models, are attractive in terms of simplicity and computation. However, such models are normally built around the still water level as an equilibrium point and assume small movement, leading to poor model validity for realistic WEC motions, especially for the large amplitude motions obtained by a well controlled WEC. The method proposed here is to use an adaptive algorithm to estimate the control model online, whereby system identification techniques are employed to identify a linear model that is most representative of the actual controlled WEC behaviour. Using exponential forgetting, the linear model can be regularly adapted to remain representative in changing operational conditions. To that end, this paper presents a novel adaptive controller based on a receding horizon pseudospectral formulation. A case study is presented, providing an preliminary evaluation of the adaptive receding horizon pseudospectral control (ARHPC), using simulations based on both linear hydrodynamic modelling and computational fluid dynamics (CFD). The parameter adaptation is shown to behave as expected in both different simulation environments. The ARHPC is observed to perform well in irregular sea states, absorbing more power than its non-adaptive counterpart, and having smaller motions and power-take off forces.

Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.

Numerical wave tanks (NWTs) provide efficient test beds for the numerical analysis at various stages during the development of wave energy converters (WECs). To ensure the acquisition of accurate, high-fidelity data sets, validation of NWTs is a crucial step. However, using experimental data as reference during model validation, exact knowledge of all system parameters is required, which may not always be available, thus making an incremental validation inevitable. The present paper documents the numerical model validation of a 1/20 scale Wavestar WEC. The validation is performed considering different test case of increasing complexity: wave-only, wave excitation force, free decay, forced oscillation, and wave-induced motion cases. The results show acceptable agreement between the numerical and experimental data so that, under the well-known modelling constraints for mechanical friction and uncertainties in the physical model properties, the developed numerical model can be declared as validated.