Modelling of nonlinear wave-buoy dynamics using constrained variational methods

Kalogirou, Anna, Bokhove, Onno and Ham, David (2017) Modelling of nonlinear wave-buoy dynamics using constrained variational methods. In: Proceedings of the ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering, 7A . ASME.

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Abstract

We consider a comprehensive mathematical and numerical strategy to couple water-wave motion with rigid ship dynamics using variational principles. We present a methodology that applies to three-dimensional potential flow water waves and ship dynamics. For simplicity, in this paper we demonstrate the method for shallow-water waves coupled to buoy motion in two dimensions, the latter being the symmetric motion of a crosssection of a ship. The novelty in the presented model is that it employs a Lagrange multiplier to impose a physical restriction on the water height under the buoy in the form of an inequality constraint. A system of evolution equations can be obtained from the model and consists of the classical shallow-water equations for shallow, incompressible and irrotational waves, and relevant equations for the dynamics of the wave-energy buoy. One of the advantages of the variational approach followed is that, when combined with symplectic integrators, it eliminates any numerical damping and preserves the discrete energy; this is confirmed in our numerical results.

Item Type: Book Section
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 05 Oct 2017 05:11
Last Modified: 19 Sep 2020 00:03
URI: https://ueaeprints.uea.ac.uk/id/eprint/65081
DOI: 10.1115/OMAE2017-61966

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