## 3 Results
### Pressure Characteristics of the Sedan Surface  
To evaluate the divergence in predictive capabilities among various turbulence modeling approaches concerning the sedan's aerodynamic load, Figure 11 shows the temporal progression of the pressure coefficient at measurement points on the front door surface, both on the windward and leeward sides of the sedan. Six typical moments (\(t_{1}\), \(t_{2}\), \(t_{3}\), \(t_{4}\), \(t_{5}\) and \(t_{6}\)) before and after the sedan drives into the dune are marked in Figure 11, and they are used as the time pitchings for the subsequent study of the transient evolution of the vortex structure. Figures 12 and 13 present the respective distributions of the pressure on the sedan surface before and after (moments \(t_{1}\) and \(t_{4}\)) driving into the dune section at the speed of 100 km/h on the basis of turbulence modeling approaches RNG \(k\)-\(e\), LES, and IDDES, and the time interval of the sedan driving within the dune section is marked using an orange dashed line. Figure 11: The time history curves of the pressure at the measurement points predicted by the three turbulence modeling approaches: (**a**) windward side; (**b**) leeward side. As shown in Figure 11a, the prediction results of the three turbulence modeling approaches for the pressure coefficient at the measurement point on the windward of the sedan are consistent at \(t_{1}\). The evolutionary trend in the pressure obtained by three turbulence modeling approaches basically coincides after the sedan enters the dune section, but some deviations in the amplitude of the pressure fluctuations exist. As shown in Figure 11b, the evolutionary trend in the pressure at the measurement points obtained by RNG \(k\)-\(\epsilon\) model is identical to the LES model, but the RNG \(k\)-\(\epsilon\) model fails to capture small fluctuations in the pressure. The absolute value of the pressure coefficient at the measured point on the leeward calculated by IDDES is higher than corresponding values calculated by LES. The variation amplitude of the pressure on the windward calculated by the RNG \(k\)-\(\epsilon\) and IDDES models differs from corresponding values obtained from the LES model  
Figure 12: Pressure distribution of the sedan surface at the \(t_{1}\) moment: **(a)** RNG \(k\)-\(\epsilon\); **(b)** LES; **(c)** IDDES (Subscripts 1, 2, 3, and 4 indicate the windward, leeward, top view, and bottom view of the sedan, respectively; the blue dashed line marks the main differences in pressure distribution in the results). Figure 13: Pressure distribution of the sedan surface at the \(t_{4}\) moment: **(a)** RNG \(k\)-\(\epsilon\); **(b)** LES; **(c)** IDDES (Subscripts 1, 2, 3, and 4 indicate the windward, leeward, top view, and bottom view of the sedan, respectively; the blue dashed line marks the main differences in pressure distribution in the results). by 0.054 and 0.333 (3.45% and 21.3%), respectively, when the sedan is driving within the dune section. Regarding the leeward measurement points, the variation amplitude of the pressure coefficient in the RNG \(k\)-\(\varepsilon\) and IDDES simulations differs from those in the LES by 0.546 and 0.053 (33.17% and 3.22%), respectively. As shown in Figure 12, the results obtained by the RNG \(k\)-\(\varepsilon\), LES, and IDDES models regarding the pressure distribution on the top and windward surfaces of the sedan at time \(t_{1}\) are almost the same. However, the predictions made by these three models for the pressure distribution on the leeward surface of the sedan show some variations. In the RNG \(k\)-\(\varepsilon\) simulation, a large negative pressure zone is observed in the head of the leeward, failing to represent the detailed features of the pressure distribution in the middle and tail areas. Although the IDDES model captures the differences in the pressure distribution between the small areas at the rear doors on the leeward, it is less capable of describing the differences in more detail than the LES model.