# Research on the Water Entry of the Fuselage Cylindrical Structure Based on the Improved SPH Model
## 4 Numerical Simulation of Water Entry of a Cylinder Structure  
### Validation through Numerical Simulation  
To demonstrate the accuracy of the improved SPH model in this paper, this section simulates the water entry of an elastic cylinder structure. The model is consistent with the literature [55]. The water domain has a width of 1 m and a height of 0.4 m, and the radius of the cylinder is 0.1 m. The particle spacing is 0.005 m. The density of the elastic cylinder is 1100 kg/m\({}^{3}\), the modulus is 1.2 \(\times\) 10\({}^{7}\) N/m\({}^{2}\), the Poisson's ratio is 0.4, and the sound speed is 104 m/s. The initial velocity of the cylinder is 2.33 m/s.  
Figure 4 displays the isotropic pressure of the elastic cylinder and water obtained via the traditional SPH and improved SPH models. It is observed that the pressure distribution under the traditional SPH is chaotic, while both the pressure of the cylinder and water exhibit a uniform distribution under the improved SPH model. The results show that the improved SPH model can greatly improve tensile instability. From Figure 4b, at the initial water entry stage, the pressure is at its maximum near the interface. As the elastic cylinder continues to enter the water, the isotropic pressure of the elastic cylinder converts into a tensile force, and the pressure of the water propagates downward. Figure 5 provides a comparison of the slamming force experienced by the cylinder obtained from the simulation [55], theory [56], and experiment [57]. The peak value of the slamming force in our simulation is in good agreement with that in the theory and experiment, with an error of 0.024, compared to a peak value error of 0.047 in [55], which validates the computational accuracy of the improved SPH model in this paper. It is also found that, in the theoretical solution and the experiment, the slamming force of the cylinder rises rapidly during water entry, which is faster than that in the simulation. The reason may be that when the slamming force reaches its peak value obtained from the theory and experiment, the depth of the cylinder in the water at this moment is less than the particle spacing of 0.005 m in our simulation, so the simulation cannot be entirely accurate. In [55], it is also indicated that the smaller the spacing is, the faster the slamming force rises.  
Figure 4: Isotropic pressure of the elastic cylinder and water obtained via the traditional SPH and improved SPH methods. (**a**) Traditional SPH. (**b**) Improved SPH.  
Next, simulation is performed for the water entry of a skin cylinder. Then, the simulation is conducted for the skin-stringer structure and skin-stringer-floor-column structure. Due to the large physical size of the object and the large number of particles, GPU-accelerated computing is used in this paper. Figure 6 describes the single-GPU parallel flowchart for the SPH method, which shows the main computational part in the GPU, and the CPU only plays the roles of input and output. After initialization, the program transfers the particle information (coordinates, velocity, density, etc.) to the GPU, and the results are transferred back from the device to the host, only reaching the output step.