# Study on the Influence of a Rigid Wall on Cavitation in Underwater Explosions Near the Free Surface
## 1 Introduction  
The occurrence of cavitation during underwater explosions is an important phenomenon. The formation of cavitation domains significantly influences the propagation of underwater explosion loads and the resulting loads on structures. Furthermore, the shock loads generated by cavitation collapse can lead to a reloading effect on the surrounding structures, making the analysis and prediction of the impact responses of structures during underwater explosions more complex. Cavitation during underwater explosions is a phenomenon accompanied by the formation of cavities. Unlike common hydrodynamic cavitation, cavitation in underwater explosions is primarily caused by an intense rarefaction wave action, and the collapse of cavitation can cause damage to underwater structures and equipment [1; 2; 3]. Currently, the evolution mechanism of cavitation in underwater explosions, especially its development and collapse mechanisms, as well as the characteristics of cavitation collapse loads, lack clear understanding. There is also a lack of widely accepted models for cavitation collapse loads, which to some extent hinders the improvement ofthe naval vessel blast resistance design and operational efficiency. Since the 1940s, the importance of cavitation effects on ship damage has been recognized. Foreign research institutions and scholars have conducted a series of studies on cavitation phenomena during underwater explosions, yielding a wealth of research outcomes that have laid a solid foundation for subsequent in-depth investigations. However, the understanding of cavitation evolution and collapse mechanisms as well as the characteristics of cavitation collapse loads remain unclear, demanding further research efforts in order to enhance the effectiveness of the naval vessel blast resistance design and utilization [4; 5; 6; 7]. Early simulation methods for cavitation in underwater explosions were initially limited by the state of development in computational fluid dynamics and computational resources. The primary focus centered on the cavitation finite element (CAFE) method ([PERSON] and Deruntz) [8; 9; 10]. These researchers utilized [PERSON]'s cavitation method based on the CAFE to investigate the impact of fluid cavitation on the structural response. While the CAFE method demonstrated stability in predicting cavitation in underwater explosions, its computational requirements were excessive for three-dimensional models. To overcome these limitations, [PERSON] proposed the cavitating acoustic spectral element (CASE) method to enhance the computational efficiency of cavitation [9; 10]. Subsequently, both the CAFE and CASE methods have been integrated into commercial software codes [11; 12]. However, the theoretical assumptions of the acoustic finite element approach impose constraints, limiting its applicability to qualitatively analyze cavitation under weak shock wave conditions in the far field of underwater explosions. Its primary advantage lies in rapidly predicting the initiation time and approximate range of cavitation, but it cannot accurately forecast the evolutionary process and internal characteristics of the cavitation domain [13; 14; 15; 16]. In contrast, interface tracking methods assume the existence of a distinct interface between the liquid and vapor phases of water and employ an iterative procedure to capture this interface [17; 18]. The qualitative analysis of cavitation under weak shock wave conditions in far-field underwater explosions primarily focuses on predicting the initiation time and approximate range of cavitation, without accurately forecasting the evolution process and internal characteristics. This analysis method is typically based on the theoretical assumptions of the acoustic finite element theory, which postulates the existence of a distinct interface between the liquid and vapor phases and employs an iterative process to capture this interface.