## 2 Fluctuating Pressure Analysis of Idealized Side Mirror
### Incompressible Numerical Simulation  
The whole computational domain is divided into several regular regions by the block method in the integrated computer engineering and manufacturing (ICEM). The hexahedral mesh is used, and the boundary layer mesh is created on the surface of the side mirror. The final number of grid elements is about 7 million and the quality of the mesh is very good. Near-wall layer extrusions is built to resolve the boundary and adverse-pressure-gradient flow separation with fine mesh. The minimum mesh size is 0.001 m and meets the requirement of at least six elements per wavelength. Figure 3 shows the results of meshing in the computational domain. The fluctuating pressure distribution of airflow through the side mirror is calculated by using the software FLUENT. The airflow velocity is 40 m/s, and the inlet condition is velocity-inlet. Meanwhile, the turbulence length scale \(L\) and turbulence intensity \(I\) are set as \(L=0.07D\) and \(I=u^{\prime}/\overline{u}=0.16(Re)^{-1/8}\). \(u^{\prime}\) and \(u^{\prime}\) are the turbulent fluctuating velocity and the average velocity. \(Re\) is the Reynolds number calculated by characteristic dimension \(D(Re=\rho vD/\mu)\). \(\rho\) is the air density at 1.225 kg/m\({}^{3}\). \(v\) is the current speed. \(\mu\) is the aerodynamic viscosity at \(1.7894\times 10^{-5}\). For the set of the boundary conditions of the model, the outlet condition is pressure outlet at 0 Pa because the reference pressure is 1 atmospheric pressure. The turbulence length scale L and turbulence intensity I at the outlet are set to be the same as that at the inlet. The setting of boundary conditions is shown in Table 2.  
The highest frequency of the calculation is \(10,000\) Hz, time step size \(t=2e-5\) s, and the total time is 0.22 s. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Boundary Name** & **Boundary Condition** & **Value** \\ \hline Inlet & Velocity-inlet & 40 m/s \\ Outlet & Pressure-outlet & 0 Pa (Relative pressure) \\ Side mirror & No-slip wall & - \\ ground & No-slip wall & - \\ Other surface & Symmetric & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Settings of boundary conditions. Figure 3: Result of meshing in computational domain. Figure 2: (**a**) The position relationship between the panel and the side mirror (**b**) The distance between the receiver point and the panel. The pressure distribution nephogram of the bottom panel of the side mirror is shown in Figure 4. We can see that the local pressure in front of the side mirror is high and forms a horseshoe vortex. The pressure on the left and right side and the back of the side mirror is relatively low. The pressure distribution on the back of the side mirror is uneven and there is vortex. Figure 5 shows the velocity vector and local enlarged drawing of \(Y=0\) section. We can see that the presence of the side mirror results in a lower airflow velocity on the back of the mirror, and the air velocity around is higher. Because of the airflow velocity difference, the high-speed airflow flows continuously to the region of low-speed airflow and forms counter-current and vortices. The maximum velocity occurs on the top of the side mirror surface, about 62 m/s, which is 30%-50% higher than the velocity of the flow field. After the top, the airflow gradually separates from the side mirror. Instead of following the radian of the side mirror, it extends backward along the horizontal direction and results in a separation zone. The length of the separation zone is about two times the length of the side mirror. Then the airflow contacts the ground again and results in the re-attachment zone. Figure 5b clearly shows the velocity changes around the side mirror. The periodic vortex shedding phenomenon at the junction of the side mirror and the ground causes the fluctuating pressure of the surrounding air to change continuously with time. Figure 4: Distribution of pressure at the bottom panel of the side mirror. Figure 5: (**a**) Velocity vector map of the side mirror.