# Study on the Influence of a Rigid Wall on Cavitation in Underwater Explosions Near the Free Surface
## 4 Conclusions  
This paper explores the characteristics of cavitation and atomization induced by underwater explosions near the free surface using a multiphase flow model based on the two-fluid phase transition approach. The numerical method employed in this study allows for the modeling of phase transitions between the liquid and vapor phases during the propagation of shock waves and rarefaction waves in underwater explosions. The influence of a rigid wall on the cavitation evolution process and the cavitation collapse load is investigated under different conditions, including variations in the charge quantity and water depth. The study also examines the evolution of important physical qualities such as the density, pressure, and cavitation domain within the flow field. By analyzing the computational phenomena and summarizing the results, several conclusions can be drawn:  
1. The presence of a rigid wall significantly affects the cavitation evolution process in underwater explosions. It influences the shape, size, and dynamics of the cavitation domain, as well as the interaction between the explosion and the surrounding fluid.
2. The cavitation collapse load is influenced by the existence of a rigid wall. The collapse time and collapse pressure of the cavitation domain are significantly different compared to the free-field condition. These differences arise from the interaction between the reflected wave on the wall and the cavitation collapse load.
3. The size and position of the cavitation domain undergo notable changes under different operating conditions. The proximity of the rigid wall leads to distinct patterns in the cavitation domain evolution, resulting in variations in the pressure distribution and the emergence of new cavitation regions.  
Figure 19: Pressure–time history curve of the measurement point at distances of 4 m (**a**) and 8 m (**b**) from the symmetry axis, at a depth of 2.0 m from the free surface.  
Figure 18: Comparison of the volume evolvement in cavitation domain under two cases.  
By investigating these phenomena and analyzing the computational results, this study provides valuable insights into the behavior of cavitation and atomization induced by underwater explosions near the free surface. The findings contribute to a deeper understanding of the complex dynamics involved, aiding in the development of safety measures and protective strategies in marine and underwater engineering applications. It is important to note that several conclusions presented in this paper are qualitative in nature and derived from two-dimensional models. Although the cases presented demonstrate numerous merits and the model itself is time consuming and reliable, there is still room for further improvement. Future research endeavors will focus on incorporating three-dimensional models, fluid-structure interactions, adaptive mesh refinement, and detonation reactions to enhance the accuracy and comprehensiveness of the findings.  
Conceptualization, J.Y., X.Z. and Y.X.; methodology, J.Y., Y.Z. and L.Z.; software, J.Y. and Y.Z.; validation, J.C. and Y.X.; formal analysis, J.C.; investigation, Y.Z.; resources, J.Y. and Y.X.; data curation, L.Z.; writing--original draft preparation, J.Y.; writing--review and editing, X.Z.; visualization, J.C.; supervision, X.Z.; project administration, J.Y. and X.Z. All authors were involved in the preparation of the manuscript. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The data that support the finding of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.