Highly nonlinear phenomena in the dynamics of a floating body is one of the important research themes in our section. Numerical computations in this research must be done in the time domain, using mainly Mixed Eulerian Lagrangian (MEL) method. The MEL method makes it possible to satisfy the exact free-surface boundary condition under the assumption of inviscid fluid with irrotational motion. Therefore, this method has been applied to nonlinear water wave probelms and recently being extended to the wave-body interaction problems and more complicated 3-D problems.
The final goal in this study is development of a computer code which can simulate large-amplitude motions of a 3-D body in severe waves. Right now, we are studying 2-D problems in order to understand fundamental mechanism and get some numerical know-hows.

A numerical method under development is featured in that:
  1. A higher-order panel method using isoparametric elements is employed, which is capable of pursuing precisely the particle movement near the intersection point between the body and free surfaces.

  2. A numerical wave absorbing beach is incorporated in the scheme to avoid the wave reflection from the outside numerical boundary (see the above figure).

  3. At each time step, the temporal derivative of the velocity potential in the pressure equation is computed accurately by solving the boundary-value problem for the acceleration field in addition to the problem for the velocity field.

Comparisons with experimental results have been carried out for 1) linear, second- and third-order forces on a 2-D body induced by the forced oscillation test, and 2) the time history of free oscillations of a body in regular waves.

Examples of the results of 2) are shown in the right figure, in which we can see favorable agreement. Extension to 3-D probelms and taking viscous effects into account will be the research topics in the future.

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