Abstract
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.