## 3 Unsteady Flow Analysis and Decomposition of Surface Pressure  
### Unsteady Flow Analysis  
To ensure the convergence of the unsteady simulation, the aerodynamic drag \(C_{d}\) was used, defined in the following form:  
\[C_{d}=\frac{D}{0.5\rho u^{2}S}, \tag{44}\]  
where \(D\) is the drag force, \(\rho\) is the air density, \(u\) is the flow velocity, and \(S\) is the reference cross-section area. The air density and the reference area were 1.225 kg/m\({}^{3}\) and 0.85 m\({}^{2}\), respectively. Figure 5 shows the predicted time history of the drag coefficient of HSM. It  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equations** & **Discretization Method** & **Remarks** \\ \hline Inlet boundary & Velocity inlet & 30.56 m/s, nonreflecting \\ Outlet boundary & Pressure outlet & 101,325 Pa, nonreflecting \\ Side and upper boundary & Pressure far field & 101,325 Pa, Ma = 0.09 \\ Ground boundary & No-slip wall & \\ HSM wall & No-slip wall & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details on applied boundary conditions.  
Figure 4: Grid description of computational domain in \(x\)-\(z\) plane.  
Figure 3: Target model of Hyundai Simplified Model (HSM) and entire computational domain: (**a**) overall shape of HSM with related geometric dimensions; (**b**) dimensions of computational domain with boundary conditions applied, where H denotes the height of the HSM.  
was found that the oscillation magnitude became slightly lower after \(t=2.8\) s. On the basis of this observation, the simulation result was determined to be converged after \(t=2.8\) s, and flow simulation data after \(t=2.8\) s were used for further analysis.  
Figure 6 shows the instantaneous iso-contours of velocity magnitude and static pressure at the central vertical plane. The entire computation domain was seen to be sufficiently large such that the strong wake flow generated behind the HSM was convected and left the computation domain without any spurious reflection from the boundary, which is of critical importance for successful aeroacoustic simulation.  
Figure 7 shows the instantaneous iso-surface of the Q-criterion. It is seen that the strong turbulent flow separations from the A-pillar produced complex vortex structures, which in turn characterized the flow field disturbance around the side window. Figure 8 shows the reattachment line of the A-pillar vortex on the left window. The reattachment angle was found to be between 25\({}^{\circ}\) and 30\({}^{\circ}\), which is in good agreement with the PIV (particle image velocimetry) measurements [7]. It reveals that fluid flow around the A-pillar had a strong swirling structure and induced the most large-scale coherent surface pressure fields on the side window. Figure 9b-f compare the power spectral density (PSD) of surface pressure between the predicted and measured values at the five sensor positions shown in Figure 9a. The measured data were taken from a previous study [7]. The PSD of simulated surface pressure fluctuations was obtained at a sampling frequency of 80,000 Hz by averaging 21 blocks of 8192 samples (0.1024 s) weighted by a Hanning window, with 80% overlap. It can be seen that there was excellent agreement between the two groups of results at all monitoring points, although underestimations were observed in the high-frequency range higher than \(\sim\)3.5 kHz, for which the current grid and time resolutions seemed to be insufficient to resolve small vortex eddies responsible for the flow and acoustic disturbances in the corresponding high-frequency band.  
Figure 5: Calculated time history of aerodynamic drag of HSM.  
Figure 6: Snapshot of iso-contours of (**a**) velocity magnitude and (**b**) static pressure (at \(y=0\) m, \(t=2.8\) s).