Towards optimization of a wave-to-wire energy device in a breakwater contraction

A wave-to-wire mathematical and numerical model is explored for a wave-energy device ideally integrated within a breakwater. It consists of a wave-focussing contraction, a wave-activated buoy and an electromagnetic power generator. The model with all its integrated components has previously been derived from first principles in wave hydrodynamics, constrained (vertical) buoy motion and the 3D Maxwell equations for the electromagnetic generator (the latter using the axisymmetry of the set-up and thin-wire approximations). By revisiting this model, the following novelties are presented: (i) dispersive longwave dynamics is included at similar computational costs as, and in extension of, the nondispersive shallow-water dynamics considered numerically hitherto, via inclusion of so-called Benny-Luke wave dynamics; (ii) improvements have been made to modelling the power generator and the numerical formulation of the coupled, monolithic system of wave-, buoy and electro-dynamics; and, (iii) a series of simulations of the new shallow-water and Benney-Luke wave-energy models are presented, exploring the resonance characteristics of the system under varying wave amplitudes and frequencies. It turns out that it is better to directly use a potential flow model because it can be made consistent like the shallow-water model, whereas the Benney-Luke model cannot. Finally, it is discussed how the modelling set-up is well-suited for further optimization using both the reduced wave-energy model as well as surrogate modelling.