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.
Modelling of Nonlinear Wave-Buoy Dynamics Using Constrained Variational Methods
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Kalogirou, A, Bokhove, O, & Ham, D. "Modelling of Nonlinear Wave-Buoy Dynamics Using Constrained Variational Methods." Proceedings of the ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. Volume 7A: Ocean Engineering. Trondheim, Norway. June 25–30, 2017. V07AT06A060. ASME. https://doi.org/10.1115/OMAE2017-61966
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