This thesis investigates advancements to the mathematical and numerical modelling of a novel wave-energy device, currently in development. The work establishes rigorous theoretical frameworks, develops efficient computational tools, and provides insights to support device design and optimisation.
A fully nonlinear three-dimensional potential flow model is derived from first principles using a Lagrangian framework. This approach provides a rigorous and flexible framework, enabling systematic linearisation, consistent coupling of reduced-dimension hydrodynamic models to device constraints, and the incorporation of additional physical components, such as a capacitor in the electromagnetic generator.
The depth-averaged two-dimensional \acl{BL} model is critically assessed. While offering improved dispersive accuracy over the classical \acl{SW} approximation, the \acl{BL} formulation is shown to be incompatible with the fundamental coupling between the buoy and free surface, demonstrating that increased model fidelity does not necessarily mean practical suitability for coupled device simulations. The \acl{SW} model is therefore justified on both computational and physical-consistency grounds.
A flexible computational framework for solving the linearised \acl{SW} equations is developed, built with the Firedrake finite-element library and incorporating a novel approach for subdomain handling. The resulting algorithm significantly outperforms previous implementations, enabling fast simulations, parameter sweeps and surrogate-based optimisation studies to be carried out in practical time frames.
An analytical model of the buoy–generator subsystem is studied, yielding explicit expressions for power output which allow direct assessment of design parameters and identification of practical strategies for performance enhancement, including alternative coil configurations and control approaches.
Together, these contributions provide a coherent framework linking theoretical formulation, reduced-order modelling, numerical simulation, and device-level design insights, advancing both the understanding and practical analysis of the device, and supporting its continued development. Future work includes experimental validation, nonlinear and 3D code extensions, exploration of alternative reduced-order models, and the application of advanced control strategies to maximise power output.
