Floriane Gidel, Yang Lu, Onno Bokhove, Mark Kelmanson

A new, cost-effective and widely applicable tool is developed for simulating three-dimensional (3D) water-wave motion in the context of the maritime-engineering sector, with specific focus on the formation and analysis of extreme waves generated within in-house experimental wave tanks. The resulting ``numerical wave tank'' is able to emulate realistic sea states in which complex wave-wave or wave-beach interactions occur. After first transforming the time-dependent free surface and oscillatory wavemaker into a static rectilinear domain with fixed boundaries, a variational approach is used to derive weak formulations that lead to a non-autonomous space-discrete Hamiltonian system to which robust (stable and mass-conserving) temporal integrators are applied. Specifically, first-order symplectic-Euler and second-order Stormer-Verlet schemes are implemented in the finite-element environment ``Firedrake'', and convincing validation of the new tool is demonstrated via a comparison of its numerical results with data post-processed from real wave-tank experiments at the Maritime Research Institute Netherlands (MARIN). Current and future extensions to industrial applications are discussed.