## 3 Geometric Model, Computational Mesh, and Physical Parameter  
### Geometric Model  
Figure 1 shows a simplified geometric model of a jack-up offshore platform and its seabed foundation. The jack-up platform is not permanently fixed at one place, but temporarily fixed at a place for a certain purpose, such as satellite launch. Since there is no mooring system, the jack-up platform can only be used in offshore areas. It can be seen in Figure 1 that the jack-up offshore platform is composed of four pile legs (labeled as No. 1, 2, 3, and 4 in Figure 1b), and an upper box-type platform. The four legs are thin-walled steel pipe piles with a diameter of 4 m, and the pipe wall thickness is 8 cm. The height of the pile legs is 80 m, of which 3 m of the pile tips can be inserted into the offshore seabed foundation to fix the whole platform structure. A disc with a thickness of 8 cm and a radius of 6 m is set on each pile leg at a position that is 3 m away from the pile tips (note: the position of the disc along the pile leg is adjustable in the practical structure design). When the seabed foundation is relatively soft, these discs can significantly increase the contact area with the seabed foundation, and thus can greatly enhance the vertical bearing capacity of the seabed foundation. This type of structural form is generally referred to as \"spudcan\" in the offshore oil industry. The horizontal distance from the center of the pile legs to the edges of the box-type platform is 18 m. The length and width of the box-type platform, which is hollow, are both 66 m, its height is 8 m, and the thickness of  
the steel plate used to make the box-type platform is 2 cm. The jack-up platform can be driven by itself or towed by tugboats to a predetermined position on the sea. During this process, the four pile legs are in a stowed state, and the hollow pile legs and the upper platform could provide sufficient buoyancy during navigation. After the jack-up platform arrives at the predetermined position, the four pile legs are gradually lowered and inserted into the seabed foundation to provide sufficient bearing capacity, and make the platform structure more stable under the action of ocean waves, which is conducive to the successful completion of the tasks for the offshore platform, e.g., satellite launch. The length of the seabed foundation is 246 m, the width is 100 m, and the depth is 50 m. The shortest distance from the center of the four pile legs to the left and right seabed boundary is 98 to 118 m, and the shortest distance to the front and back seabed boundary is 35 m. This distance is more than eight times the diameter of the pile legs. The adverse effects of the fixed lateral boundary of the seabed on the dynamic response of the seabed around the offshore platform can be eliminated as much as possible. Figure 1: _Cont._  
ments, which would have a disastrous impact on some tasks for the jack-up platform, such as the satellite launch. Therefore, this study does not investigate the stability of the jack-up platform under very extreme waves, but focuses on some conventional ocean waves. In the modeling, the third-order Stokes wave theory is used to generate the target wave trains. The motion of ocean waves is controlled by the VARANS equation, and the RNG \(k\)-\(\varepsilon\) turbulence model is adopted to describe the turbulence in the wave field. Furthermore, the end of the computation domain is set as the wave-absorbing boundary, to avoid the reflection of incident waves at the end boundary of the fluid domain.