## 4 Validation of Numerical Methods
### Verification of the Wedge Breaking into Water  
To verify the accuracy and feasibility of the ALE method used to analyze fluid-structure coupling problems, a simulation and test of the wedge breaking into the water are carried out using this method. Then, the simulation results are compared with the test results.  
Taking the hollow wedge made of Q235 steel as the research object, a test of the vertical water entry of the wedge is carried out using self-developed test tooling. The test model is shown in Figure 6. Its dimensions are 0.4 m in length, 0.2 m in width, 0.1 m in height, and 0.05 m in thickness; the angle of inclination is \(60^{\circ}\) and the data acquisition system is DH5925N. The test tooling mainly consists of a bracket and electromagnet. A high-speed video camera is used to observe the details of the wedge entering the water, and acceleration sensors are symmetrically placed in two locations to test whether the wedge enters the water vertically and from a height of 0.2 m.  
For the vertical water entry test, it is necessary to ensure that the wedge remains vertical as it enters the water. Symmetrically distributed acceleration sensors are used to estimate verticality due to the uniform mass distribution of the wedge. In addition, since the water surface is static, when both acceleration sensors register similar data, it indicates that the wedge is perpendicular to the water surface upon entry.  
As seen in Figure 7, when the wedge enters the water, both the time of peak acceleration arrival and the size of peak acceleration are the same on both sides. In addition, observations  
Figure 5: Spherical simulation of rigid plate impact and variation in ISO theoretical ice pressure with area.  
Figure 6: Wedge test model.  
from the high-speed camera show no deflection, confirming that the wedge enters the water vertically.  
For the numerical simulation, the wedge model used is identical to the one used in the test, and the material is treated as a rigid body, though the fluid domain is appropriately reduced. The size of the water domain is 0.8 m \(\times\) 0.4 m \(\times\) 0.4 m, while the size of the air domain is 0.8 m \(\times\) 0.4 m \(\times\) 0.1 m. The mesh size is 1 mm and hexagonal, and the material is defined using \"MAT_NULL. The simulation model diagram is shown in Figure 8.  
The fluid domain is modeled using the Eulerian algorithm, while the wedge is modeled by the Lagrangian algorithm. The keywords \"LINER-POLYNOMIAL and \"EOS-GRUNEISEN are used to realize the equations of state of the air and water, respectively. Their parameters are shown in Section 3.2. Non-reflective boundaries are adopted to prevent the wall surface from affecting the simulation results of the wedge entering the water.  
The test results are shown in Figure 9. The peak magnitude of the wedge's inflow acceleration, the overall trend of the curve, and the inflow time are consistent with the test values, which proves the feasibility of the ALE method in dealing with the wedge inflow problem.  
Figure 8: Simulation model diagram of wedge entering the water.  
Figure 7: Wedge acceleration test values.  
Figure 9: Testing for wedge entering water and simulation acceleration results.