## 3 Setting and Verification of Numerical Simulation Strategy
### Glide Simulation Setup  
The calculation domain division of the gliding simulation example in this paper is shown in Figure 14, which is roughly the same as that of the self-propulsion simulation. Except that the longitudinal axis of the hybrid-driven underwater glider body is at a 12\({}^{\circ}\) angle with the direction of the inflow, the other settings were the same as that of the self-propulsion simulation. Similar to the determination of the grid base size of the self-propulsion simulation, propellers Kap01 and Kap04 were selected to match the diamond wing underwater glider, and the grid-independent analysis of the glide simulation was carried out.  
In this example, the inlet velocity is 0.5 kn (0.2572 m/s), which was calculated by the SST \(k\)-\(\omega\)+\(\gamma\) transition turbulence model, Schnerr-Sauer cavitation model, and VOF gas-liquid two-phase method. The calculated values of the overall resistance D, overall lift L, propeller resistance D_propeller, and propeller lift L_propeller of the hybrid-driven underwater glider are shown in Figures 15 and 16, respectively, for the changes in the total number of grids in the example, from which it can be seen that the total number of grids tends to be stable when greater than 4 \(\times\) 10\({}^{6}\) in the grid independence verification of the hybrid-driven underwater glider. The corresponding relationship between the total number of grids and the size of the grid foundation is shown in Tables 6 and 7, respectively. When  
Figure 14: Calculation domain division of glide simulation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Base Size** & **0.16D** & **0.13D** & **0.08D** & **0.07D** & **0.064D** \\ \hline Total mesh (\(\times\)10\({}^{6}\)) & 1.764 & 2.565 & 4.758 & 6.103 & 7.288 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The corresponding relationship between the mesh base size and the total number of mesh in the calculation example with propeller Kap04.  
Figure 13: \(y^{+}\) distribution of self-propulsion simulation of diamond wing AUG with propeller Kap01 (**a**) and Kap04 (**b**).  
the size of the grid foundation is less than 0.1D, the numerical results of the simulation calculation tend to be stable.  
The \(y^{+}\) distribution of the glide simulation example when the grid base size is 0.08D is shown in Figure 17, and the \(y^{+}\) values are limited to 0-3.2 and 0-1.5, respectively.  
Considering the accuracy and time cost of the simulation calculation, the base mesh size of 0.08D was selected uniformly in the gliding simulation in this study.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Base Size** & **0.3D** & **0.18D** & **0.12D** & **0.1D** & **0.08D** \\ \hline Total mesh (\(\times 10^{6}\)) & 0.932 & 1.691 & 3.251 & 4.228 & 5.234 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Correspondence between the mesh base size and the total mesh size of the diamond wing UG+ propeller Kap01 gliding simulation example.  
Figure 16: Grid independence verification for the glide simulation of diamond wing UG + Kap04, overall drag D, and overall lift L (**a**), propeller drag D_propeller and lift L_propeller (**b**).  
Figure 15: Grid independence verification for the glide simulation of diamond wing UG + Kap01, overall drag D, and overall lift L (**a**), propeller drag D_propeller and lift L_propeller (**b**).