## 1 Introduction  
Cavitation is the process and phenomenon of phase transition between liquid and vapor, which appears in the liquid or at the interface of liquids and solids due to hydrodynamic factors [1; 2; 3; 4; 5]. It is a complex hydrodynamic phenomenon, which has obvious unsteady characteristics, and that widely occurs in hydraulic machinery, propellers, and hydraulic engineering. Cavitation occurs when the pressure of a local liquid is reduced to a certain threshold value; for example, cavitation often occurs near turbine blades and pump blades. Cavitation often results in a reduction in efficiency and the vibration of the unit in hydraulic turbines and pumps. Thus, cavitation has become a research hotspot recently, and many researchers have been devoted to investigating cavity's occurrence, breakup, shedding, collapse, and influence factor. Due to the high costs and technical restriction of experimental investigations, in the last few years, CFD (computational fluid dynamics) have been applied to the research of cavitation. Many methods have been presented and used in cavitation investigation, and valuable achievements have been made. Most of these methods were based on the homogeneous fluid approach, i.e. the homogeneous equilibrium flow model (HEM). The two phases of vapor and liquid are considered to be a mixed fluid with variable density, and the relative velocity between the two phases is neglected. HEM considers the weighted average values of the corresponding parameters of the vapor-liquid as the parameters of the mixed fluid. Therefore, the continuity equation and momentum equation for the mixed fluid is established. There are two main methods to evaluate the variable density at present: the barotropicequation model (BEM) [6; 7] and the transfer equation-based model (TEM) for a void ratio with the source terms modeling the mass transfer due to cavitation [8; 9; 10]. Most of these homogeneous methods didn't consider the acting force between the two phases, which is not coincident with the law of physics. [PERSON] et al. [11] introduced the level set method into cavitation simulation. The level set method takes the surface tension into account, and many valuable achievements have been made. Thus, this method would be an effective way to treat the interface between vapor and water, and should be used in future research. Also, research has shown that the choice of the turbulence model plays an important role in obtaining a faithful simulation of unsteady behaviors of cloud cavitation since the flow is three-dimensional and contains many different length scales [12]. The direct numerical simulation (DNS) may get a precise result by considering all these scales, but this would require a high computing power capacity. Other available approaches used in engineering prediction areLarge eddy simulation (LES), Detached eddy simulation (DES) and Reynolds Average Navier-Stokes (RANS). LES is an increasingly popular method in cavitation simulations, and lots of work has been done using this method [13; 14; 15; 16; 17; 18]. However, the LES method also needs large computational resources. Thus, researchers developed the DES model, which combined the RANS and LES approaches. However the switch between RANS and LES is defined by the length of the largest cell size, and it is grid-sensitive. The widely used standard two-equation turbulence models (e.g. \(k\)-\(\varepsilon\) class) usually have a tendency to overpredict the turbulent viscosity in the region of cavity closure, and the models can hardly capture the shedding dynamics. For this reason, different modifications have been presented to reduce the turbulent viscosity for cavitating flow simulation. One of those modifications is to introduce a filter-based model (FBM) for better estimation of the viscosity [19]. Adaptive mathematical models immediately determined the accuracy of the numerical simulation, and the specific cavitation model may have advantages in this specific condition.