## 4 Wave-Ship Interaction and Green-Water Loads
### Ship Motion Responses and Green-Water Loads  
#### 4.4.1 Ship Motion Responses Induced by the Freak Wave  
To ensure result accuracy, grid independence testing must be conducted beforehand. Given the complexity of wave-ship interactions, it is preferable to select larger computational domains while maintaining a fine simulation of the flow field, thereby effectively reducing the impact of wave reflection caused by the boundary. As such, the present study utilized nested mesh methods, dividing the mesh region into two parts: background and free surface regions, with the free surface regions being denser. Through these methods, computational speed was maximized while maintaining result accuracy. Three types of meshes were tested, including coarse mesh (background region mesh size of 2 m \(\times\) 2 m \(\times\) 2 m, free surface region mesh size of 1 m \(\times\) 1 m \(\times\) 1 m), medium mesh (background region mesh size of 1 m \(\times\) 1 m \(\times\) 1 m, free surface region mesh size of 0.5 m \(\times\) 0.5 m \(\times\) 0.5 m), and fine mesh (background region mesh size of 0.5 m \(\times\) 0.5 m \(\times\) 0.5 m, free surface region mesh size of 0.25 m \(\times\) 0.25 m \(\times\) 0.25 m). Simulation time steps were determined according to the Courant number criterion ([PERSON] and [PERSON] [37]), with values of 0.1 s, 0.05 s, and  
Figure 8: A sketch of pressure monitoring points on the deck.  
Figure 9: A sketch of pressure monitoring points on the breakwater.  
0.025 s used for the coarse, medium, and fine meshes, respectively. As shown in Figure 10, the results of the grid-independence tests indicate that the medium mesh size provides a balance between simulation accuracy and computational speed.  
Since present study focuses on the interaction between freak waves and the ship, the following content examines only the period from when a freak wave appears until the interaction with the ship concludes. Specifically, this refers to the time interval between 530 s and 565 s in Figure 7 (hereinafter, 0 s corresponds to 530 s in Figure 7).  
As shown in Figure 11, at 13.4 s, the freak wave comes in touch with the ship bow, causing the wave to roll over due to the large bow flare. Subsequently, a substantial amount of water surges over the deck at an extremely high speed. During this process, the ship bow is lifted by the freak wave. At 15.7 s, the on-deck water slams the breakwater and rapidly moves upwards along its surface. At 16.6 s, the water climbs to the highest point, with some of it overtopping the breakwater. Following this, the water drains off the deck, marking the end of the first green water impact. At this moment, the ship bow is greatly lifted, with increased heave motion reaching the maximum value, and the pitch motion also increasing to the first peak value. Additionally, then, the freak wave moves towards the middle of the ship, and the amplitude of the heave and pitch motions decreases as the ship gradually returns to its normal floating state. As the freak wave approaches the stem of the ship, the stern is gradually lifted, causing the ship bow to sink into the water. At 27.0 s, the bow is submerged below the free surface. At 29.20 s, a small amount of water surges over the deck, leading to the second green water impact but far less than the first. At this moment, the absolute value of the pitch motion reaches its maximum. As the freak wave propagates across the ship, the interaction between the freak wave and the ship ends at about 34.0 s.  
Figure 10: Results of grid independence test: (**a**) Heave; (**b**) pitch; (**c**) peak pressure of deck; (**d**) peak pressure of breakwater.