# Morphological Analysis of a Collapsing Cavitation Bubble near a Solid Wall with Complex Geometry
## 1 Introduction  
Cavitation occurs when the local pressure becomes less than a liquid's saturated vapor pressure. The bubble collapse that happens near a solid wall can severely damage the neighboring solid surface owing to the resulting high velocities, pressure, and temperature [1]. In addition, the bubble experiences inward deformation, micro-jet formation, collapse, or multiple collapses owing to the retarding effect of the solid wall. The potential applications of cavitation have been extensively explored in material surface cleaning [2], ultrasonic therapy [3], and environmental protection [4]. The interaction mechanism between a cavitation bubble and a solid wall has an important role in various applications. In particular, when cavitation occurs near a solidwall involving a complex geometry, the profile evolution of the collapsing bubble can be more varied. The effect of the surface geometry of the solid wall on the dynamic behavior of the collapsing bubble has been experimentally investigated [5; 6; 7]. A complex boundary can significantly alter the dynamic behavior of cavitation bubbles, such as the bubble shape and micro-jet. However, it is difficult to investigate the interaction mechanism between bubbles and solid walls with arbitrarily complex geometries because of the limitations of experimental methods, e.g., experimental conditions cannot be changed at any time. Numerical methods have been adopted to efficiently simulate cavitation bubble collapse near a solid wall and investigate the dynamic bubble collapse process. Conventional numerical simulation methods include the finite volume method (FVM) [8; 9], the boundary element method (BEM) [10], and the finite element method [11]. [PERSON] et al. [9] investigated the dynamic process of a vapor bubble collapse near a rectangular groove wall using the FVM and the volume of fluid (VOF) method. [PERSON] and [PERSON] [10] adopted the BEM to investigate the dynamics of a spark-generated bubble that oscillated near a circular aperture in a curved rigid plate. However, these macroscopic numerical methods require other approaches to track or capture gas-liquid interfaces, such as the VOF [12] and level set method [13], which may reduce computational efficiency. In implementing the complex geometry boundaries, it is difficult for these macroscopic models to choose approximate functions in each discrete unit to characterize changes in arbitrarily complex boundaries. Over the past few decades, the lattice Boltzmann method (LBM), has been developed as a powerful tool for simulating multiphase flow problems [14; 15; 16; 17; 18; 19]. The LBM based on the discrete Boltzmann equation with the simplified collision operator can model phase segregation and interfacial dynamics in multiphase flows with collision and streaming steps [15]. The mesoscopic approach has multiple unique advantages such as high efficiency, completely parallel algorithms, and the simplicity of programming. Generally, the multiphase models in the LBM include four kinds of different models, i.e., the color-gradient [20], pseudopotential [21; 22; 23], free-energy [24], and phase-field models [25]. The pseudopotential model proposed by [PERSON] and [PERSON], is also named as Shan-Chen (SC) model. In this model, an interparticle potential is proposed to simulate the interactions between the fluids, from which a non-monotonic equation of state (EOS) can be obtained. As a result, the interface can be formed automatically, and the pressure can be calculated from the EOS efficiently. [PERSON] and [PERSON] [26] first introduced the Shan-Chen LBM into the cavitation field and concluded that applications to more complex problems should be possible. Later on, several scholars devoted themselves to investigating the cavitation phenomenon with the pseudopotential LBM [27; 28; 29; 30; 31]. Meantime, the LBM has good spatiotemporal flexibility in dealing with boundary conditions, which enables the easy introduction of solid boundaries with complex geometries into numerical models. [PERSON] et al.