## 3 Numerical Simulations
### Numerical Method  
The Mach number \(M\) is 0.15, the static temperature of freestream \(T\) is 300 K, the dynamic viscosity \(\mu\) is 1.0474 \(\times\) 10\({}^{-5}\) Pa \(\times\) s, the air density is 1.225 kg/m\({}^{3}\), and the characteristic length \(c\) is 1 m. The pressure-based solver is used with the coupled algorithm [32]. The gradients are computed according to the least-squares cell-based method. Gradients are needed not only for constructing values of a scalar at the cell faces, but also for computing secondary diffusion terms and velocity derivatives. Ansys Fluent affords cell-based and node-based schemes. The node-based scheme is known for being more accurate, particularly on skewed unstructured meshes. However, it is relatively more expensive than the cell-based scheme. Considering the limited computing resources and the applied structured meshes, the least-squares cell-based scheme is selected, which can provide comparable accuracy to that of the node-based scheme and is less expensive. The standard gradient limiter (default TVD slope limiter) [33] is adopted to prevent spurious oscillations, which uses the Mimmod function (minimum modulus) to limit and clip the reconstructed solution overshoots and undershoots on the cell faces. The second-order scheme is used for interpolating the pressure values at the faces, which reconstructs the face pressure using a central differencing scheme. It should be pointed out that for the Spalart-Allmaras turbulence model, the simulation results of modified turbulent viscosity applying first-order upwind seem little better than those applying second-order upwind. Taking the sharp trailing edge and adopting Spalart-Allmaras at far-field distances of 12 m and 16 m as examples, we chose three AOAs (0\({}^{\circ}\), 2\({}^{\circ}\), 4\({}^{\circ}\)); the comparative data are shown in Table 3. At an AOA of 2\({}^{\circ}\), although the \(C_{l}\) error ratio of the second-order at a far-field distance of 12 m is lower than that of the first-order, the total error ratios of the first-order are preferred. Therefore, we choose the modified turbulent viscosity of Spalart-Allmaras as the first-order upwind. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Mesh (Cells)**} & \multicolumn{8}{c}{**Angle of Attack (\({}^{\circ}\)) and Experiment Data of \(C_{d}\) and \(C_{l}\)**} \\ \cline{2-13}  & \multicolumn{4}{c}{**(C\({}_{d}\),\(C_{l}\)and Error Ratios)**} \\ \cline{2-13}  & \multicolumn{2}{c}{**0\({}^{\circ}\)**} & \multicolumn{2}{c}{**2\({}^{\circ}\)**} & \multicolumn{2}{c}{**4\({}^{\circ}\)**} & \multicolumn{2}{c}{**6\({}^{\circ}\)**} & \multicolumn{2}{c}{**8\({}^{\circ}\)**} & \multicolumn{2}{c}{**10\({}^{\circ}\)**} \\ \cline{2-13}  & **0.00809** & **0** & **0.00816** & **0.2125** & **0.00823** & **0.4316** & **0.00885** & **0.6546** & **0.0105** & **0.8873** & **0.01201** & **1.0707** \\ \hline \multirow{3}{*}{400,000} & 0.00791 & Approx. 0 & 0.00836 & 0.21990 & 0.00911 & 0.43983 & 0.01044 & 0.64020 & 0.01243 & 0.84399 & 0.01529 & 1.03809 \\ \cline{2-13}  & 2.28\% & / & 2.42\% & 3.48\% & 10.63\% & 1.91\% & 17.95\% & 2.20\% & 18.37\% & 4.88\% & 27.29\% & 3.05\% \\ \hline \multirow{3}{*}{590,000} & 0.00799 & Approx. 0 & 0.00823 & 0.21747 & 0.00893 & 0.43380 & 0.01013 & 0.64718 & 0.01192 & 0.85506 & 0.01437 & 1.05464 \\ \cline{2-13}  & 1.19\% & / & 0.82\% & 2.34\% & 8.48\% & 0.51\% & 14.44\% & 1.13\% & 13.54\% & 3.63\% & 19.36\% & 1.50\% \\ \hline \multirow{3}{*}{840,000} & 0.00801 & Approx. 0 & 0.00831 & 0.21750 & 0.00904 & 0.43375 & 0.01034 & 0.64685 & 0.01231 & 0.85387 & 0.01515 & 1.04991 \\ \cline{2-13}  & 0.29\% & / & 1.80\% & 2.35\% & 9.83\% & 0.50\% & 16.78\% & 1.18\% & 17.20\% & 1.50\% & 26.11\% & 1.94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grid independency study of three levels of different mesh with error ratios at a far-field distance of 12 m.