# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 3 Validation and Convergence Analysis of Numerical Methods  
### Validation and Convergence Analysis of Numerical Methods for the SUBOFF Submarine  
The size of the computational domain directly impacts the number of grids, computational time, and accuracy of the numerical simulation. Therefore, following the ITTC [31] guidelines, the entire computational domain for the submarine is set as a rectangular cuboid. The inflow boundary is set along the horizontal \(X\)-axis as the velocity inlet, the outflow boundary is set as the pressure outlet, and the remaining boundaries are set as the slip wall. The dimensions of the computational domain in the length, width, and height directions are as follows: \(-6<X/L_{sub}<1.5\), \(-2<Y/L_{sub}<2\), and \(-2<Z/L_{sub}<2\). The computational domain division and boundary conditions are illustrated in Figure 4.  
After the computational domain is established, the mesh is generated using the mesh generation module provided by the software. A prism layer mesh is applied to the boundary layer on the surface of the model, while a trimmed mesh is used for the rest of the domain. A schematic of the mesh division is shown in Figure 5. Considering the influence of the number of grids on the computational results, a mesh convergence verification is performed using three different base sizes. The overall grid density of the computational domain is adjusted by changing the basic size of the mesh. For refining the mesh around the  
Figure 4: Submarine model calculation domain setting. Figure 3: The process of determining the self-propulsion point during submarine model self-propulsion simulation. submarine body, a surface mesh refinement method is used, dividing the surface into three parts: the sail, the tail rudders, and the hull. Three mesh sets are used in the study, with grid counts of 3.89 million, 8.38 million, and 17.6 million, respectively. The boundary layer mesh consists of 10 layers, with a \(Y\) + value of 30. At present, the total resistance experimental values proposed by the Naval Surface Warfare Center (NSWC) Carderock Division in 1998 are widely used as a reference for numerical simulations [30]. In this study, a velocity of 3.051 m/s was selected for grid independence and convergence validation. The results of unsteady resistance calculation are compared with experimental values, and the comparison results are shown in Table 1. In Table 1, as the number of grids increases, the error decreases, and the difference in resistance is not significant between 8.38 million and 17.6 million grids. During the grid convergence validation process for submarine hull resistance, the convergence analysis was conducted using the grid convergence validation process discussed by [PERSON] et al. [32] and [PERSON] et al. [33]. The analysis results are presented in Table 2. In Table 2, \(R_{G}\), \(P_{G}\), and \(U_{G}\) represent the grid convergence rate, estimated accuracy, and grid uncertainty, respectively. As indicated in Table 2, the grid convergence rate \(R_{G}\) for the submarine hull resistance calculation is less than 1, indicating that the grid exhibits monotonic convergence. The grid uncertainty is 0.7159, which is relatively small, suggesting that the numerical simulation uncertainty for the submarine model is within a reasonable range, and the numerical calculation results are relatively reliable. By balancing calculation accuracy and efficiency, the medium grid was selected for subsequent research. In addition to the grid independence and convergence study, to verify the reliability of the numerical simulation method in this section, the straight-ahead resistance of the fully appended SUBOFF submarine model at various velocities was calculated and compared with the experimental data from reference [30]. The comparison results are shown in Figure 6. As can be seen from Figure 6, the overall numerical simulation results of the submarine model resistance align well with the experimental values.