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


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.

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