## 3 Analysis of Wind Field Results over the Hill
### Comparison of Mean Wind Fields with Different Turbulence Models
Our results are roughly consistent with the results of the mean wind field simulated by [PERSON] and [PERSON] [23] with the downburst flowing over flatlands. [PERSON] and [PERSON] [23] compared LES with various RANS turbulence models and found that LES and REA had better results. In this paper, the simulation effects of LES, DES, and RANS are given, namely, LES is approximately equal to REA and greater than DES, which provides a more comprehensive reference for turbulence model selection. It also shows that in the numerical simulation of the mean wind field of downbursts over flatlands and hills, the effects of the LES and \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Error** & **LES** & **DES-SST** & **DDES-SST** & **IDDES-SST** & **DES-RK** & **DES-SA** & **REA** & **SST** & **RNG** \\ \hline
10\% & 50\% & 31.43\% & 28.57\% & 44.29\% & 41.43\% & 38.57\% & 57.14\% & 38.57\% & 40\% \\ \hline
20\% & 71.43\% & 50\% & 45.71\% & 74.29\% & 70\% & 51.43\% & 75.71\% & 54.29\% & 70\% \\ \hline
30\% & 84.29\% & 64.29\% & 61.43\% & 81.43\% & 81.43\% & 67.14\% & 85.71\% & 71.43\% & 81.43\% \\ \hline MNB & \(-\)3\% & \(-\)15.94\% & \(-\)15.86\% & \(-\)2.83\% & \(-\)3.85\% & \(-\)13.47\% & 2.04\% & 2.95\% & 5.94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of velocity error between different turbulence models and the experiment. REA turbulence models are relatively consistent. They are not affected by conditions such as flat lands or hills. In addition, the conclusion that REA is better than RNG and SST in the RANS simulation method is consistent with the results of [PERSON] et al. 's [25] numerical simulation of a downburst flowing over a flatland and [PERSON] et al. 's [29] numerical simulation of a downburst flowing over a hill. It further shows that the simulation effect of the turbulence model is not affected by terrain conditions. Figure 10 presents the dimensionless mean wind velocity contours (\(u/u_{j}\)) obtained from each turbulence model. The figure shows a consistent overall distribution trend of the mean wind velocity among the models. An acceleration effect near the ground is noticeable from the hillside on the windward side to the hilltop. At the hilltop, the simulation results of the DES-SST, DDES-SST, and IDDES-SST turbulence models exhibit essentially the same acceleration regions, with ranges slightly smaller than those of other models. Notably, the SST model portrays a larger acceleration region than all the other models. Meanwhile, at the foot of the hill on the leeward side, the computed results of the DES-SST, DDES-SST, and DES-SA models reveal conspicuous zones of low wind velocity. Further, the computed distributions using the LES, SST, RNG, and REA models at locations farther away from the hill on the leeward side are similar, indicating a greater wind velocity than that at locations corresponding to other models. These findings suggest that the DES-SST, DDES-SST, and IDDES-SST turbulence models are preferable for the simulation of hill terrain flows in situations involving an acceleration effect near the ground, whereas the SST model may overestimate the acceleration region. Conversely, the DES-SST, DDES-SST, and DES-SA models may better predict low wind velocity regions. Figure 9: Horizontal wind velocity error at the hilltop of each turbulence mode. Figure 10: _Cont._