## 3 Analysis of Wind Field Results over the Hill
### Comparison of Mean Wind Fields with Different Turbulence Models
simulated wind velocity is greater than 30%. Comparing different DES turbulence models in Figure 8b,e,f, it can be seen that the results of DES-RK are within an error range of 10%, with more distribution points and a higher accuracy. Comparing different RANS turbulence models in Figure 8g-i, it can be seen that the error distribution of wind velocity values obtained by the SST model is wide, while that obtained by the REA model is distributed within a 10% error range, indicating that the REA model has better results than other RANS models. In summary, for different SST turbulence models, their accuracy is ranked as IDDES-SST \(>\) DES-SST \(>\) DDES-SST \(>\) SST; for different DES turbulence models, their accuracy is ranked as DES-RK \(>\) DES-SST \(>\) DES-SA; and for different RANS turbulence models, their accuracy is ranked as REA \(>\) RNG \(>\) SST. Figure 8: Comparison of velocity error between different turbulence models and the experiment. (**a**) LES mode; (**b**) DES-SST model; (**c**) DDES-SST model; (**d**) IDDES-SST model; (**e**) DES-RK model; (**f**) DES-SA model; (**g**) REA model; (**h**) RNG model; (**i**) SST model. To evaluate the accuracy of different turbulence models, Table 3 presents the percentage of data points, where the difference between the simulated wind velocity (obtained from different turbulence models) and the experimental wind velocity falls within error ranges of 10%, 20%, and 30%. Additionally, the table includes the Mean Normalized Bias (MNB) for both models. The MNB represents the mean relative error between the simulated and experimental wind velocities and is defined as follows. \[\text{MNB}= \frac{1}{N}\sum_{i=1}^{N}\left(\frac{V_{i,fitting}-V_{i,exp}}{V_{i,exp}}\right) \tag{12}\]  
where \(N\) is the number of measurement points in the experiment and \(V_{i,exp}\) and \(V_{i,fitting}\) are the wind velocity values obtained from the experiment and turbulence models, respectively. MNB is the metric that can synthetically characterize the degree of change in the data. When the MNB is negative, the simulated wind velocity is smaller than the experimental wind velocity as a whole, and when the MNB is positive, its wind velocity is larger than the experimental wind velocity. An analysis of the errors reveals that approximately 85% of the results from the LES and REA models fall within a 30% error range. The largest discrepancy between the simulated wind velocity (obtained from the DES-SST and DDES-SST models) and the experimental wind velocity is observed. In general, all turbulence models, except for the RANS model, underestimate the experimental wind velocity. Focusing on the hilltop location, the error values of the wind velocity at this location are analyzed for different turbulence models. Figure 9 shows that when the wind velocity values at near-surface locations are large due to the acceleration effect at the hilltop, the results of each turbulence model fall within a 10% error range. When the wind velocity values are small, the wind velocity obtained from the RNG, SST, and DES-SA models is smaller than the experimental wind velocity, with error confidence intervals within 20%. In summary, the LES and REA turbulence models provide the most accurate simulation results for the mean wind field on a hill, followed by the DES turbulence model. Based on the above research, in the numerical simulation of the mean wind field of the downburst over the hill, a more detailed simulation effect of the turbulence model is given. In different SST turbulence models, the accuracy effect is IDDES-SST \(>\) DES-SST \(>\) DDES-SST \(>\) SST; in different DES turbulence models, the accuracy effect is DES-RK \(>\) DES-SST \(>\) DES-SA; and in different RANS turbulence models, the accuracy effect is REA \(>\) RNG \(>\) SST. On the whole, the effect of the turbulence model on the simulation results of the mean wind field on hills is investigated. It is found that the REA turbulence model is comparable to the LES simulation results, followed by the DES turbulence model.