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Spectral-domain models are a relatively efficient method of producing an estimate of the expected response and power capture for wave energy converters (WECs) that are subject to nonlinear forces such as Coulomb (constant) or viscous (quadratic) damping. They are generally faster than time-domain models and more accurate than frequency-domain models. However, these models can only be used for spectral excitation and are not appropriate for use with monochromatic waves. The estimates of the expected responses and power captures are made using the assumption that the individual frequency components in the wave spectra are uncorrelated. Because the results of a spectral-domain model are fundamentally statistical they are not able to provide details of extreme values. The only spectral-domain models that have so far been implemented effectively linearize the nonlinear forces and iterate the linearized equations of motion to determine the expected response. This technique has been validated using time-domain models and wave-tank experiments. The linearization of the WEC dynamics effectively assumes that the response is Gaussian; however, spectral-domain modelling techniques used in other fields suggest that it should be possible to model non-Gaussian responses, which is expected to increase the range of nonlinearities for which there are solutions in the spectral domain.

In general it is possible to extend modelling techniques that are used for modelling single wave energy converters (WECs) to model WEC arrays; it is simply correctly defining the geometric layout and degrees-of-freedom. Indeed, these multiple degree-of-freedom array models are the most common method used for modelling WEC arrays. However, in addition to any issues associated with the particular modelling technique, there are additional issues that need to be considered when modelling WEC arrays. For models based on linear potential flow theory, where the hydrodynamic coefficients are generated using a boundary element method (BEM), it is important to recognize that the computational effort increases approximately with the square of the number of degrees-of-freedom. In addition, in a WEC array model it is also important to model all the degrees-of-freedom of each WEC (for single WECs the nongenerating modes are often legitimately ignored). Another issue with these models is that the number of frequency components required to accurately generate the impulse response function also increases as does the required duration of the impulse response function. Consequently, the models are typically limited to small arrays of up to about 10 devices. In computational fluid dynamics (CFD) models, the computational effort does not increase significantly with the number of WECs, but with the volume of fluid that needs to be modelled. Thus, depending on the spatial extent of the WEC array this could result in a significant increase in the computational requirements. However, perhaps more significantly, internal numerical dissipation could be an issue for some CFD array models because it would become difficult to separate the WEC array interactions from the numerical dissipation.

Models of wave energy converter (WEC) arrays that use phase-averaged wave propagation models, also called spectral wave models, rely on the conservation of action (energy) density, which propagated across a grid of points. The action density is defined as the spectral energy density divided by the wave frequency and is used (rather than the energy density) because this is conserved in the presence of marine currents; however, they are equivalent in still water. In a spectral wave model the action (energy) density is propagated using linear wave theory, with energy added and removed through source terms. In a standard spectral wave model these source terms include wave breaking, white-capping, bottom friction, wind growth, triad, and quadruplet wave–wave interactions; WECs or wave farms can be added as additional source terms. The WECs or wave farms can be represented using either a supragrid or subgrid model. In a supragrid model the WEC or wave farm is represented as a boundary that spans one or more grid points, with the wave action redistributed based on the characteristics defined by the supragrid model, which is normally defined with reflection, absorption, and transmission coefficients. In a subgrid model each WEC is defined by a single grid point, with the wave action redistributed based on transmission, absorption, and diffraction/radiation coefficients (which may be defined using Kochin functions). Although a phase-averaged wave propagation model can be used to model the interactions between WECs in an array, or to determine the distal effects of a wave farm, a separate model is required to define the characteristics of the supragrid or subgrid model. Thus, these models are best described as hybrid models. Although WEC arrays have been modelled in phase-averaged wave propagation models, there further development is required; in particular, there has been very little validation of these models, which is an area where further work is required.