# Morphological Analysis of a Collapsing Cavitation Bubble near a Solid Wall with Complex Geometry
## 1 Introduction
[32; 33] simulated the collapse process of a single bubble near a plane solid wall and between two parallel solid walls. [PERSON] et al. [34] and [PERSON] et al. [35] both used a multi-relaxation-time (MRT) pseudopotential model to simulate dual-bubble collapse near a rigid boundary. It can be found that the relative position of two bubbles plays an important role in the bubble near-wall collapse process. [PERSON] et al. [36] simulated the cavitation bubble near a curved wall using the MRT-SC model and discussed the influence of bubble-wall distance on bubble collapse. [PERSON] et al. [37; 38] investigated the influence of a rectangular bulge solid wall and hydrophobic concave corner on cavitation bubble collapse from the evolution of physics fields. The geometry of the solid wall significantly influences bubble collapse. However, previous studies have considered the complex geometries of solid walls as periodic shapes with equal widths [9; 37]. This cannot account for certain characteristics of actual complex solid walls, such as sections and cracks. Thus, it is necessary to accurately model actual complex solid walls. In contrast to the solid walls in previous works, the arbitrarily complex geometry solid walls have more complex geometries. To reflect the differences between the solid walls, the fractal dimension is adopted to quantitatively describe the complexity of a solid wall, and it increases with the complexity. Various processes occur when a cavitation bubble collapses near a solid wall with a complex geometry. Further research is required on the methods for describing the cavitation bubble near-wall collapse process and the effect of the solid wall on the collapsing bubble considering the large amount of data obtained from the bubble collapse process, various complex configurations, and evolutions of physical fields. The Minkowski functionals-based morphological analysis method (Min-MAM) [39] has been introduced to investigate complicated physical fields. [PERSON] and [PERSON] [40; 41] introduced the Minkowski functionals to describe the morphological evolution of homogeneous phases during spinodal decomposition. [PERSON] et al. [42] characterized the density and velocity fields of the phase separation process in a complex fluid using the Minkowski functionals. They clarified the effect of the temperature field on phase morphology and spinodal decomposition. [PERSON] et al. [43] conducted a detailed review of the Minkowski functionals and adopted them to explore the complex procedure of shock wave reaction on porous material. The Min-MAM is an efficient tool for analyzing and acquiring effective information in complicated physical fields [44; 45; 46]. Therefore, the Min-MAM can potentially be adopted to quantify the profile evolution of collapsing bubbles. In this study, we introduce a solid wall with an arbitrarily complex geometry and investigate the dynamic bubble collapse process. The pseudopotential MRT-LBM is adopted to establish the collapse model of a cavitation bubble in the vicinity of a solid wall with an arbitrarily complex geometry. Furthermore, the fractal dimension and Min-MAM are used to quantitatively describe the complexity of the solid wall and the evolution of bubble morphology. The interaction mechanism between a cavitation bubble and a solid wall is investigated by changing the surface complexity, geometric features of the solid wall, and position offset parameter. In general, this study systematically investigates the effect of solid walls with arbitrarily complex geometries on the bubble collapse process. The morphological evolution of the collapsing bubble is described with quantitative measures, which provides an alternative tool for analyzing the cavitation bubble near-wall collapse process. The remainder of this paper is organized as follows. The pseudopotential MRT-LBM and Min-MAM are presented in Section 2. The numerical simulation model and dynamic bubble collapse process are described in Section 3.