## 2 Numerical Simulation
### Meshing and Irrelevance Analysis  
Mesh delineation is the basis for subsequent simulation calculations, and the quality of the mesh will have a direct impact on the simulation results. Unstructured meshes are more randomly distributed, simple and fast to generate, flexible, and can be adapted to a variety of complex geometries, but there is also the problem of poor quality local meshing,  
Figure 1: Computational domain assembly model.  
resulting in poor overall mesh quality, large quantities, and a long computational solution time. The structured mesh requires a block topology of the model, which will lead to a more complex and time-consuming mesh division, but considering its regular node distribution, it can better save computational solution time and achieve convergence accuracy faster. Therefore, this paper adopts the structured meshing method for meshing. Figures 2 and 3 show the meshing results.  
In order to reduce the influence of the number of grids on the accuracy of the calculation, a grid-independent analysis was carried out, as shown in Table 1. The head and efficiency of Program2 are taken as unit 1, and the head and efficiency of all other Programs are compared with Program2. When the number of grids in the full flow channel reaches 4 million, the head and efficiency tend to stabilize, and the relative head error between Program 3 and Program 4 is 0.25% and the relative efficiency error is 0.17%. In view of the computer configuration and calculation time, the division of Program 3 was finally determined as the standard for dividing all models. The following describes the different quality metrics of this model: The average aspect ratio refers to the average of the aspect ratios of all the grid cells in the whole model. In this model, the mean aspect ratio is 1.91, which indicates that most of the grid cells have relatively close aspect ratios and that the overall shape of the grid is more balanced. The mean warping factor indicates the degree of deformation of the shape of the grid cells. In this model, the average warping factor is 0.002, which indicates that most of the grid cells are relatively well shaped with no obvious deformation or distortion. The maximum top angle, which refers to the largest angle in the grid cell, ranges from 60\({}^{\circ}\) to 130\({}^{\circ}\). This indicates that the grid cells are reasonably shaped, with no angles that are too sharp or too flat. The tilt, which is used to assess the degree of deformation of the grid cells, ranges from 0 to 0.75. More than 80% of the grid cells have tilts less than 0.5, which indicates that most of the cells are relatively stable and do not  
Figure 3: Boundary layer mesh refinement.  
Figure 2: Meshing of the whole model.  
deform excessively. The orthogonality coefficient is used to measure the perpendicularity of the grid lines to their neighbors and has an average value of 0.89. The fact that more than 83% of the cells have orthogonality coefficients greater than 0.75 indicates that the majority of the cells have good orthogonality, and the grid lines are relatively perpendicular. Taken together, the division of Program 3 seems to perform better in most of the quality indicators when computer configuration and computation time are considered and can be used as a criterion for dividing all models.