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Modelling of Nonlinear Wave-Buoy Dynamics Using Constrained Variational Methods

[+] Author Affiliations
Anna Kalogirou

University of East Anglia, Norwich, UK

Onno Bokhove

University of Leeds, Leeds, UK

David Ham

Imperial College London, London, UK

Paper No. OMAE2017-61966, pp. V07AT06A060; 10 pages
doi:10.1115/OMAE2017-61966
From:
  • ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 7A: Ocean Engineering
  • Trondheim, Norway, June 25–30, 2017
  • Conference Sponsors: Ocean, Offshore and Arctic Engineering Division
  • ISBN: 978-0-7918-5773-1
  • Copyright © 2017 by ASME

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.

Copyright © 2017 by ASME

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