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Variational coupling of nonlinear water wave and ship dynamics: continuum and finite element modelling

Banff International Research Station for Mathematical Innovation and Discovery

We report on the mathematical and numerical modelling of (non)linear ship motion in (non)linear water waves. We derive a coupled model for the wave-ship dynamics following a variational methodology, in order to ensure zero numerical damping which is important for wave propagation. The final system of evolution equations comprises the classical water-wave equations for incompressible and irrotational waves, and a set of equations describing the dynamics of the ship. The novelty in our model is in the presence of a physical restriction on the water height under the ship, which is enforced through an inequality constraint via a Lagrange multiplier. The model is solved numerically using a variational (dis)continuous Galerkin finite element method with special, new and robust time integration methods. Here we aim to show numerical results for the dynamics of the coupled system in a hierarchy of increasing complexity: linear water-wave and linear ship dynamics, and potentially also fully coupled (non)linear water-wave and nonlinear ship dynamics.

Mathematics; Fluid mechanics; Partial differential equations; Fluid dynamics

video/mp4

Author affiliation: University of Leeds

2017-05-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61492

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/