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A new wave-to-wire wave-energy model: from variational principle to compatible space-time discretisation

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GCS - Geometry, compatibility and structure preservation in computational differential equations

Amplification phenomena in a so-called bore-soliton-splash have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-activated buoy motion and magnetically-induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Most importantly, we develop a novel wave-to-wire mathematical model of the combined wave hydrodynamics, wave-activated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is subtly solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LED -loads, are added a posteriori. New is also the intricate and compatible (finite-element) space-time discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised wave-energy model are encouraging, yet suboptimal, and involve a first study of the resonant behaviour and parameter dependence of the device.



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