Variational and numerical modelling strategies for cost-effective simulations of driven free-surface waves

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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.



Engineering, Physical Sciences and Mathematics


water waves, variational numerical models, finite elements, verification and validation test cases, rogue waves


Published: 2022-06-17 17:18


CC BY Attribution 4.0 International

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