A time-domain BEM for instantaneous interaction by two ships head-on encountering in incident waves

Multi-ship encountering results in complex interactions that significantly modify the surrounding flow field, particularly in the presence of incident waves. Due to the disturbing effect of the complex wave system, the behavior of each ship during the encounter is influenced by the wave characteristics and the relative motions between the ships. This paper establishes a model for ship-to-ship encountering in incident waves using the time-domain Rankine Boundary Element Method (BEM). The transient responses and wave field of ships are investigated. The approach is based on the global fixed system dealing with complex external wavefields and dynamics, moment-to-moment iterative updating of the computational grid simulates the two-ship encountering, using the fourth-order Runge-Kutta method for time integration. The classical Wigley III is chosen to calculate and better validate the numerical results for a two-ship encountering in calm water and a single-ship advancing in an incident wave based on the time-domain method. On this basis, a study is carried out to investigate the transient motion and instantaneous wave field of two ships encountering toward an opposite direction in incident waves. Sensitivity analyses of parameters such as wave characteristics, transverse distance between ships, ship-to-ship speed ratio, and water depths reveal that the transient motions of ships are closely related to the incident wave characteristics. Notably, the encounter frequency differs when two ships advance in opposing directions, with variations in transverse distance, speed ratio and water depths significantly affecting the amplitude and frequency of their motions during the encounter.