The velocity is positive towards lee, and negative towards the incoming waves. It mostly consists of the slowly varying ship drift, together with sway and roll motions oscillating with the wave period. The black curve (V YDMG) shows the horizontal velocity of the center of the damage opening on the ship side. The hydrostatic contributions in calm water and waves are non-linear and are based on calculations with NAPA software. The hydrodynamic contributions are based on linear strip theory and on those based on the water motions in internal compartments. The roll and surge motions are determined by the time integration of the non-linear equations of motion coupled with the other four degrees of freedom. For the ship heave, pitch, sway, and yaw motions, the method uses response amplitude operators (RAO) determined in the frequency domain with a linear strip method. The flow rates through the breaches are based on Bernoulli’s equation. For all cases in this study, SWEs were used to model the flow on the trailer deck, and the pendulum model was used for the more deeply flooded compartment spaces below. Floodwater in internal compartments and on decks can be modeled either with shallow-water equations (SWE) or with a pendulum model. The in-house version of the Rolls code, HSVA Rolls, was used in all computations. This study sheds light on the question of how relevant is it to use the more complicated formulations instead of the very simple and robust Bernoulli model in the numerical simulation of damaged ships in the sea. Some alternative formulations are possible. ![]() Thus, there are some approximations involved in the use of the Bernoulli equation for this purpose. This equation takes neither the floodwater inertia in the opening into account nor does it regard the effect of ship motions on the flow in the opening. In many numerical simulation codes for ship survivability, the water inflow and outflow through a damage opening are modeled with Bernoulli equation, which describes steady flow in an inertial frame of reference. ![]() Recent benchmark tests show that the numerical tools for this purpose are very useful, but their accuracy and reliability still leave something to be desired. Various simulation tools are presently in use to study the behavior of damaged RoPax and cruise ships. The survivability of a damaged RoPax ship in the case of a flooding accident can be critical, as these ships have a tendency for a rapid capsize.
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