Prediction of non-linear ship responses in waves considering forward speed effects

This article describes the development of a non-linear time-domain boundary element method to determine non-linear ship responses (motions and loads) in waves. The general approach by Cummins was used to express the equation of motion in the time domain. Hydrodynamic forces were split into inertia, radiation, diffraction, Froude–Krylov and restoring components. Radiation forces were determined in time domain by convolution of the impulse response of the ship with the motion velocity. The Froude–Krylov and restoring forces were computed over the instantaneous wetted surface, taking into account ship motions, the undisturbed wave and stationary wave system. Diffraction forces were computed from the complex force amplitude resulting from the linear problem of the incident wave diffraction. The impulse response of the ship can be determined using the linear hydrodynamic damping coefficients or added masses. In this work, these two approaches were compared. Ship motions calculated with the developed method were compared with model test and RANSE-based simulations as well as with linear frequency domain results for three different ship types at various forward speeds. It was shown that the convolution integral represents the radiation forces satisfactorily. The convolution integral based on damping coefficients showed distinct advantages at zero speed. With increasing forward speed, the added mass-based convolution integral leaded in some cases to better results.