## 4 Conclusions  
This study verifies that the LES model has an accurate prediction capability of the sedan's aerodynamic characteristics when it is passing by a sand dune under crosswinds on the basis of field tests. The differences in the aerodynamic loads (lateral force, rolling moment, and yaw moment) of the sedan obtained by the RNG \(k\)-\(\epsilon\) and IDDES models were compared using the corresponding results obtained by the LES model as the benchmark. The computational cost of the LES model combined with the DPM technique is expensive, and the accuracy of computational results of the IDDES model are near those of the LES model. The calculation time for the LES and IDDES models increased by 60.0% and 11%, respectively, compared to the RNG \(k\)-\(\epsilon\) model. Finally, the effect of the wind-sands on the sedan's aerodynamic loads was discussed in conjunction with the IDDES model and the DPM technique. The main conclusions are as follows:  
1. The calculation results of the LES model on the sedan's aerodynamic loads are most consistent (4.4-7.5%) with the corresponding field measured data. The maximum differences (8.3-15.7%) exist in the lateral forces and yaw moments of the sedan obtained by the IDDES and LES models. The maximum differences between the three aerodynamic loads obtained by the RNG \(k\)-\(\epsilon\) and LES models remain between 14.8% and 18.4%. This is due to the performance difference in different turbulence models in capturing aerodynamic pressure on the sedan's surface. Further, aerodynamic loads of the sedan are obtained by integrating the aerodynamic pressures (moments of pressure against the gravity center of the sedan) of mesh cells near the sedan's surface. However, the RNG \(k\)-\(\epsilon\) model, which relies on the RANS equations for simulating turbulence, fails to capture the transient details of the pressure distribution, which leads to the discrepancy between the aerodynamic loads of the sedan predicted by the RNG \(k\)-\(\epsilon\) model with the results based on the LES and the IDDES models. 2. On the basis of the LES model, many fine vortex structures and lateral vortex structure branches are captured on the leeward of the sedan, and the subtle changes in the flow field are reflected. The model presents the details of the pressure distribution pattern in the local area of the sedan surface. 3. On the basis of the IDDES model, many vortex structures are observed on the sedan's tail and leeward, and the large vortex structures are predominant. This leads to the difference in the aerodynamic loads obtained by the IDDES and LES models. 4. The RNG \(k\)-\(\epsilon\) model captures several large vortex structures on the sedan's leeward. In particular, the number of vortex structures captured decreases after the sedan drives into the dune. On the leeward and bottom surface of the sedan, the model obtained the general characteristics of the pressure distribution without describing the details of the pressure distribution pattern in the local area. Thus, the time history changes in the sedan's aerodynamic loads are relatively smooth and do not reflect the pulsation effect of the aerodynamic loads. 5. The comparison of the wind and wind-sand cases shows that the fluctuation differences in the lateral force, the rolling moment, and the yaw moment are 8.4%, 1.1%, and 14.2%, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Types of the** & **Aerodynamic Force** & \(C_{z}\) & \(C_{mx}\) & \(C_{my}\) \\ \hline \multirow{3}{*}{Wind} & Max & 0.705 & \(-\)0.035 & 0.612 \\  & Min & 0.323 & \(-\)0.127 & 0.247 \\  & Amplitude & 0.382 & 0.092 & 0.365 \\ \hline \multirow{3}{*}{Wind–sand} & Max & 0.671 & \(-\)0.024 & 0.610 \\  & Min & 0.257 & \(-\)0.115 & 0.297 \\ \cline{1-1}  & Amplitude & 0.414 & 0.091 & 0.313 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak value and the corresponding amplitudes of the sedan’s three aerodynamic load coefficients under crosswind and crosswind–sands.