# Study on the Influence of a Rigid Wall on Cavitation in Underwater Explosions Near the Free Surface
## 1 Introduction
This method can be used to study cavitation phenomena under weak shock wave conditions, but due to the limitations of the theoretical assumptions, it cannot provide precise information about the internal details and evolutionary behavior of cavitation. This qualitative analysis approach is mainly used to quickly assess the initiation time and approximate range of cavitation, providing researchers with initial insights into cavitation phenomena. For more accurate predictions of the evolution process and internal characteristics of cavitation, more sophisticated numerical simulation methods such as interface tracking and multiphase flow methods are typically employed. These methods consider more physical processes and interactions to provide more detailed and accurate cavitation analysis results. However, these methods are computationally intensive and require more powerful computing resources and longer computation times. In summary, the qualitative analysis of cavitation under weak shock wave conditions in far-field underwater explosions mainly relies on the theoretical assumptions of the acoustic finite element theory, with a focus on predicting the initiation time and approximate range of cavitation to gain a preliminary understanding of cavitation phenomena. To obtain more accurate and detailed cavitation analysis results, more complex numerical simulation methods, as well as greater computational resources and time, are required. In recent years, compressible, multiphase fluid methodologies have gained significant attention in the field of cavitation research. These approaches consider the fluid within the cavitation domain as a homogeneous mixture existing in a saturated state [19; 20; 21; 22; 23; 24]. In these methodologies, both the liquid and vapor phases are treated as compressible fluids, and the phase transition between them plays a crucial role in cavitation generation and evolution. The interactions among water, explosion bubbles, cavitation, and air are non linear and robust, exerting a significant influence on shock wave propagation and bubble pulsation [6; 19; 25]. It is important to note that the cavitation domain induced by underwater explosions near a free surface encompasses a substantial water area and requires appropriate treatment. Accurately simulating the extremely low pressures within the cavitation zone necessitates coupling with a cavitation model. In the context of compressible fluids, two primary approaches are commonly used for cavitation simulation: the one-fluid and two-fluid methods. Several well-developed models have been proposed to simulate cavitation using one-fluid approaches, such as the cut-off mode and Schmidt model [20; 21; 22]. The isentropic one-fluid model considers the fluid as a mixture consisting of isentropic vapor and liquid phases [20]. To improve the original Schmidt model's applicability in unsteady transient cavitation flow, a modified Schmidt model was introduced [5; 23]. Furthermore, a novel isentropic cavitation model based on a reduced five-equation system was proposed specifically for investigating underwater explosion cavitation [24]. However, one significant drawback of one-fluid models is their inability to accurately capture the vapor-liquid two-phase transition during cavitation generation. To address this limitation, two-fluid models have emerged in the past decade. [PERSON] and [PERSON] developed a multiphase model based on a six-equation system that efficiently handles interfaces, cavitation, and evaporation waves [26; 27]. Another approach utilizes a four-equation system with a phase transition model to ensure thermodynamic equilibrium between the liquid and vapor phases [28; 29]. This four-equation model with phase transitions has been successfully applied to study cavitation evolution in underwater explosions, effectively capturing the physical characteristics of the flow field within the cavitation domain [13; 14].