Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method

A non-linear calculation method based on the mixed Eulerian-Lagrangian (MEL) method is presented for wave-induced motions of a two-dimensional floating body. Attention is focused on an effective calculation of the hydrodynamic force associated with the temporal derivative of the velocity potential in the Bernoulli pressure equation. Unlike other existing methods, the acceleration field can be computed simultaneously with the velocity field, which contributes greatly to a reduction in the computation time. Computations are performed for a wall-sided model and a flared model, and numerical results of the waves at upwave and downwave positions and the body motions (sway, heave and roll) are compared with corresponding experiments. The overall agreement is very good, confirming the validity of the present method. The parametric oscillation in roll, observed for the flared model, is also discussed.