## 3 Results and Discussion
### NACA0012 Models
#### 3.1.3 Results of the Sharp Trailing Edge Based on Definition Formula Applying 132 Points  
Figures 11 and 12 illustrate the distributions of \(\mathrm{P}/\mathrm{P}_{\mathrm{t}}\), \(\mathrm{T}/\mathrm{T}_{\mathrm{t}}\), and \(\mathrm{U}/\mathrm{U}_{\mathrm{t}}\) of numerical data and reference data and the corresponding mean error ratios under different locations are calculated and shown in Table 14. The optimal total mean error ratios under different configurations are displayed in Figure 13, which are highlighted in red. In terms of the far-field distance, the preferred results for the three distances are 3.14%, 2.64%, and 2.98%. In terms of the turbulence model, the minimum result of SST is 2.64%, and that of SA is 2.98%. In terms of the flux type, ROE has a finest mean error ratio of 2.64%, and that of AUSM is 3.14%. Comparing total mean error ratios for all configurations, the SST + 16 m, adopting ROE behaves the best, and the related accuracy improvements are 15.82%, 58.62%, 45.07%, 31.82%, and 11.29%, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Simulation** \\ **Configurations** \\ \end{tabular} } & \multicolumn{4}{c}{**Mean Error Ratios under Different Configurations**} \\ \cline{2-7}  & \multicolumn{3}{c}{**ROE**} & \multicolumn{3}{c}{**AUSM**} \\ \cline{2-7}  & **P/\(\mathbf{P_{t}}\)** & **T/\(\mathbf{T_{t}}\)** & **U/\(\mathbf{U_{t}}\)** & **P/\(\mathbf{P_{t}}\)** & **T/\(\mathbf{T_{t}}\)** & **U/\(\mathbf{U_{t}}\)** \\ \hline SST + 12 m & **2.28\%** & **3.96\%** & **1.04\%** & 10.41\% & 8.54\% & 4.38\% \\ \hline SA + 12 m & 4.42\% & 2.16\% & 1.90\% & 8.52\% & 3.55\% & 1.40\% \\ \hline SST + 16 m & 6.23\% & 3.25\% & 2.36\% & 5.96\% & 8.19\% & 2.07\% \\ \hline SA + 16 m & 5.33\% & 5.24\% & 1.61\% & 5.12\% & 4.57\% & 1.71\% \\ \hline SST + 20 m & 3.15\% & 4.14\% & 2.28\% & 15.30\% & 8.00\% & 2.38\% \\ \hline SA + 20 m & 4.69\% & 4.28\% & 1.73\% & 15.45\% & 9.74\% & 2.06\% \\ \hline \hline \end{tabular}
\end{table}
Table 13: The mean error ratios of \(\mathrm{P}/\mathrm{P}_{\mathrm{t}}\), \(\mathrm{T}/\mathrm{T}_{\mathrm{t}}\), and \(\mathrm{U}/\mathrm{U}_{\mathrm{t}}\) of the sharp trailing edge based on NACA4.  
Figure 10: Comparison of the simulation performances of the sharp trailing edge based on NACA4 under different simulation configurations.  
Figure 11: (a) Distributions of \(\rm P/P_{t}\) based on 132 points definition formula; (b) Distributions of \(\rm T/T_{t}\) based on 132 points definition formula.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Simulation Configurations** \\ \end{tabular} } & \multicolumn{4}{c}{**Mean Error Ratios under Different Configurations**} \\ \cline{2-7}  & \multicolumn{2}{c}{**ROE**} & \multicolumn{2}{c}{**AUSM**} \\ \cline{2-7}  & **P/\(\rm\bf\bf\bf\bf\bf\bf\bf\)** & \(\rm\rm\bf T/\rm\bf\bf\bf\bf\bf\)** & \(\rm\rm\bf U/\rm\bf\bf\bf\bf\bf\)** & \(\rm\rm\rm\bf U/\rm\bf\bf\bf\bf\)** & \(\rm\rm\rm\bf P/\rm\bf\bf\bf\bf\bf\)** & \(\rm\rm\rm\bf T/\rm\bf\bf\bf\bf\)** & \(\rm\rm\rm\bf U/\rm\bf\bf\bf\bf\)** \\ \hline SST + 12 m & 16.13\% & 9.27\% & 2.95\% & 4.32\% & 2.88\% & 2.21\% \\ \hline SA + 12 m & 8.58\% & 9.70\% & 2.41\% & 8.91\% & 6.31\% & 3.91\% \\ \hline
**SST + 16 m** & **2.14\%** & **4.21\%** & **1.57\%** & 2.78\% & 6.14\% & 1.78\% \\ \hline SA + 16 m & 11.85\% & 8.20\% & 1.66\% & 7.32\% & 5.83\% & 1.26\% \\ \hline SST + 20 m & 11.00\% & 4.36\% & 1.61\% & 4.14\% & 4.64\% & 2.83\% \\ \hline SA + 20 m & 1.76\% & 5.58\% & 1.59\% & 13.73\% & 7.50\% & 2.34\% \\ \hline \hline \end{tabular}
\end{table}
Table 14: The mean error ratios of \(\rm P/P_{t}\), \(\rm T/T_{t}\), and \(\rm U/U_{t}\) of the sharp trailing edge based on 132 points.  
Figure 12: Distributions of \(\rm U/U_{t}\) of the sharp trailing edge based on 132 points formula at location of \(\rm x/L=0.95\).