# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 4 Results and Discussions
### Case 4: Bolund Island Field Experiment (239\({}^{\circ}\) Wind Direction)
For the wind speed prediction, although there are different types of separation region shapes for the tested cases due to the different inlet conditions and hill shapes, it can be seen from Table 6 that the Mod SST \(k\)-\(\omega\) model is worse than the other models in all cases except for Case 2, where there is only one height in the experimental data; the results of the Mod RSM model are close to those of the Std SST \(k\)-\(\omega\) model, while the results of the Std RSM model are inconsistent in the four cases; it can be concluded from Case 1 that the separation region shape obtained by the Mod RSM model is closer to the experiment, whereas there is little information on the separation characteristics of Cases 2-4. Regarding the turbulence simulation, the performance of each turbulence model is consistent across the four test cases. As shown in Table 6, the Mod RSM model predicts the turbulence intensity and TKE better than the other three models. At the same time, the RSM model based on each anisotropic turbulence assumption has a larger TKE at the leeward side compared to the two-equation model, which is more consistent with the experimental results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Test Cases**} & \multirow{2}{*}{**Turbulence Model**} & \multicolumn{2}{c}{**Wind Speed**} & \multicolumn{2}{c}{**Turbulence Intensity/TKE**} \\ \cline{3-6}  & & **MAE/MAE\({}_{\text{Std SST}}\)** & **RRMSE/RRMSE\({}_{\text{Std SST}}\)** & **MAE/MAE\({}_{\text{Std SST}}\)** & **RRMSE/RRMSE\({}_{\text{Std SST}}\)** \\ \hline \multirow{4}{*}{Case 1} & Std SST \(k\)-\(\omega\) & 1.00 & 1.00 & 1.00 & 1.00 \\  & Mod SST \(k\)-\(\omega\) & 2.00 & 1.23 & 0.68 & 0.94 \\  & Std RSM & 0.33 & 0.80 & 0.76 & 0.82 \\  & Mod RSM & 1.25 & 0.99 & 0.48 & 0.89 \\ \hline \multirow{4}{*}{Case 2} & Std SST \(k\)-\(\omega\) & 1.00 & 1.00 & 1.00 & 1.00 \\  & Mod SST \(k\)-\(\omega\) & 0.03 & 0.91 & 0.19 & 0.67 \\  & Std RSM & 0.52 & 0.93 & 0.41 & 0.58 \\  & Mod RSM & 0.17 & 0.77 & 0.10 & 0.51 \\ \hline \multirow{4}{*}{Case 3} & Std SST \(k\)-\(\omega\) & 1.00 & 1.00 & 1.00 & 1.00 \\  & Mod SST \(k\)-\(\omega\) & 7.87 & 1.24 & 0.84 & 0.96 \\ \cline{1-1}  & Std RSM & 8.26 & 0.81 & 0.64 & 0.77 \\ \cline{1-1}  & Mod RSM & 1.34 & 0.80 & 0.62 & 0.76 \\ \hline \multirow{4}{*}{Case 4} & Std SST \(k\)-\(\omega\) & 1.00 & 1.00 & 1.00 & 1.00 \\  & Mod SST \(k\)-\(\omega\) & 3.18 & 1.34 & 0.62 & 0.68 \\ \cline{1-1}  & Std RSM & 0.71 & 0.96 & 0.63 & 0.79 \\ \cline{1-1}  & Mod RSM & 1.34 & 1.08 & 0.51 & 0.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistical errors of numerical results for Cases 1–4. ‘MAE\({}_{\text{Std SST}}\)’ and ‘RRMSE\({}_{\text{Std SST}}\)’ stand for the values of the Std SST \(k\)-\(\omega\) model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Turbulence**} & \multicolumn{2}{c}{**Wind Speed**} & \multicolumn{2}{c}{**TKE**} \\ \cline{2-5}  & **MAE(m/s)** & **RRMSE** & **MAE(m/s)** & **RRMSE** \\ \hline Std SST \(k\)-\(\omega\) & 0.1819 & 0.1687 & 1.5488 & 0.8312 \\ Mod SST \(k\)-\(\omega\) & 0.5783 & 0.2256 & 0.9641 & 0.5682 \\ Std RSM & 0.1289 & 0.1618 & 0.9751 & 0.6540 \\ Mod RSM & 0.2434 & 0.1824 & 0.7895 & 0.5300 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical errors of the numerical results for all masts (M1–M8, 22 in total; Bolund island case, 239\({}^{\circ}\) wind direction). In the Std SST \(k\)-\(\omega\) model and Std RSM model, \(C_{\mu}\) is the default value, i.e., 0.09, which may lead to the severe decay of the TKE in the front of the hill; therefore, this paper recommends that the Mod RSM model could change this parameter to 0.05, which shows better numerical results in the upstream. In the standard models, \(\sigma_{k}\) and \(\sigma_{\varepsilon}\) are 1 and 1.3, respectively, and, in the modified version, they are changed to 0.82 and 1, which also contribute to the accurate prediction of the wind speed on the leeward slope.