## 3 Numerical Simulations
### Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Angle of Attack (\({}^{\circ}\)) and Experiment Data of \(C_{d}\) and \(C_{l}\)**} \\  & & \multicolumn{8}{c}{**(Numerical Data of \(C_{d}\) and \(C_{l}\) with Error Ratios)**} \\ \cline{2-13}
**Type of NACA0012** & \multicolumn{8}{c}{**20 m (SST k-omega)**} & \multicolumn{8}{c}{**12 m (Spalart-Allmaras)**} \\ \cline{2-13}
**Model** & **o**\({}^{*}\) & **0.00809** & **2\({}^{*}\)** & **0.00816** & **4\({}^{*}\)** & **0.00823** & **0\({}^{*}\)** & **0.00809** & **2\({}^{*}\)** & **0.00816** & **4\({}^{*}\)** & **0.00823** \\ \cline{2-13}  & & **0**\({}^{*}\) & **0** & **0.2125** & **0.4316** & **0\({}^{*}\)** & **0** & & **0.2125** & **0.4316** & **0\({}^{*}\)** & **0.2125** & **0.4316** \\ \hline Blunt trailing edge & \(C_{d}\) & 0.00820 & 1.30\% & 0.00826 & 1.26\% & 0.00887 & 7.73\% & 0.00816 & 0.80\% & 0.00839 & 2.79\% & 0.00907 & 10.24\% \\ (Ariffol Tools 132 points) & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2201 & 3.57\% & 0.4389 & 1.68\% & Approx. 0 & 0.00\% & 0.2214 & 4.18\% & 0.4412 & 2.22\% \\ \cline{2-13} Sharp trailing edge & \(C_{d}\) & 0.00799 & 1.19\% & 0.00819 & 0.36\% & 0.00879 & 6.84\% & 0.00809 & 0.05\% & 0.00833 & 2.07\% & 0.01388 & 15.56\% \\ \cline{2-13}  & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2184 & 2.76\% & 0.4355 & 0.91\% & Approx. 0 & 0.00\% & 0.2198 & 3.45\% & 1.0560 & 1.37\% \\ \cline{2-13} Sharp trailing edge & \(C_{d}\) & 0.00800 & 1.05\% & 0.00820 & 0.50\% & 0.0080 & 6.88\% & 0.00808 & 0.18\% & 0.00830 & 1.73\% & 0.01375 & 14.47\% \\ \cline{2-13} \cline{2-13}
32 points) & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2190 & 3.07\% & 0.4370 & 1.25\% & Approx. 0 & 0.00\% & 0.2201 & 3.55\% & 1.0606 & 0.94\% \\ \cline{2-13} Sharp trailing edge & \(C_{d}\) & 0.00800 & 1.08\% & 0.00820 & 0.53\% & 0.00881 & 7.02\% & 0.00809 & 0.04\% & 0.00832 & 1.91\% & 0.01394 & 16.11\% \\ \cline{2-13}
200 points) & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2191 & 3.09\% & 0.4368 & 1.21\% & Approx. 0 & 0.00\% & 0.2198 & 3.45\% & 1.0583 & 1.16\% \\ \hline Sharp trailing edge & \(C_{d}\) & 0.00800 & 1.07\% & 0.00820 & 0.50\% & 0.00880 & 6.89\% & 0.00808 & 0.13\% & 0.00831 & 1.79\% & 0.01374 & 14.39\% \\ \cline{2-13}
264 points) & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2190 & 3.05\% & 0.4369 & 1.25\% & Approx. 0 & 0.00\% & 0.2201 & 3.56\% & 1.0606 & 0.95\% \\ \cline{2-13} Sharp trailing edge & \(C_{d}\) & 0.00800 & 1.06\% & 0.00820 & 0.51\% & 0.00880 & 6.91\% & 0.00808 & 0.15\% & 0.00830 & 1.77\% & 0.01373 & 14.32\% \\ \cline{2-13} (Formula adopts) & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2190 & 3.04\% & 0.4369 & 1.22\% & Approx. 0 & 0.00\% & 0.2200 & 3.54\% & 1.0608 & 0.92\% \\ \cline{2-13}
400 points) & \(C_{l}\) & Approx. 0 & 0.00\% & 0.2190 & 3.04\% & 0.4369 & 1.22\% & Approx. 0 & 0.00\% & 0.2200 & 3.54\% & 1.0608 & 0.92\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results of \(C_{d}\) and \(C_{l}\) with error ratios adopting SST k-omega and a far-field distance of 20 m, adopting Spalart–Allmaras and a far-field distance of 12 m.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Angle of Attack (\({}^{\circ}\)) and Experiment Data of \(C_{d}\) and \(C_{l}\)**} \\  & & \multicolumn{8}{c}{**(Numerical Data of \(C_{d}\) and \(C_{l}\) with Error Ratios)**} \\ \cline{2-13}
**Type of NACA0012** & \multicolumn{8}{c}{**12 m (SST k-omega)**} & \multicolumn{8}{c}{**16 m (SST \(k\)-omega)**} \\ \cline{2-13}
**Model** & **o**\({}^{*}\) & **0.00809** & **2\({}^{*}\)** & **0.00816** & **4\({}^{*}\)** & **0.00823** & **0\({}^{*}\)** & **0.00809** & **2\({}^{*}\)** & **0.00816** & **4\({}^{*}\)** & **0.00823** \\ \cline{2-13}  & & **0**\({}^{*}\) & **0** & **0.2125** & **0.4316** & **0** & & & **0.2125** & & **0.4316** & **0\({}^{*}\)** & **0.2125** & **0.4316** \\ \hline Blunt trailing edge & \(C_{d}\) & 0.00806 & 0.37\% & 0.00830 & 1.67\% & 0.00901 & 9.50\% & 0.00807 & 0.21\% & 0.00829 & 1.62\% & 0.00894 & 8.66\% \\ \cline{2-13} (Airfoil Tools 132 points) & \(C_{l}\) & Approx.