## 2 Fluctuating Pressure Analysis of Idealized Side Mirror
### Compressible Numerical Simulation  
In order to study the numerical calculation of the flow field of compressible fluid flowing around the side mirror, the size of the side mirror and the calculation domain are kept unchanged. Meanwhile, in order to capture the acoustic component, the mesh is partially refined. The block method is used in ICEM to divide the structural meshes into hexahedral meshes. The total number of meshes is about 19.28 million, and the minimum mesh size is 0.001 m. The boundary layer mesh is generated around the mirror surface to capture vortex characteristics. The side view of the entire computational domain grid is shown in Figure 6.  
In the material setting, the gas is set to ideal-gas, and the compressibility of the gas is considered. Viscosity is set to the Sutherland formula with three coefficients. The setting of boundary conditions is also different from that of the incompressible computation. The inlet boundary condition is set to the far-field pressure inlet. Because the Mach number is 0.118 when the velocity is 40 m/s, the inlet boundary condition is set to 0.118 and the relative pressure is set to 0 Pa. The far field of pressure is also set on the left and right sides and on the top, so that the acoustic will not produce reflex, scattering and other erroneous acoustic results [17].  
In calculation, two-equation \(k-\varepsilon\) turbulence model is used to calculate the quasi-steady solution of the flow field in 1000 steps, and then the large eddy simulation is used to calculate the unsteady flow field of the side mirror; for the sub-lattice model, the Smagorinsky-Lilly model [18] is used. The initial time step is set to \(2e-5\) s, in a single time step there are 25 iterations. After 2000 steps' calculating, the initial step is kept unchanged, and the time step is set to 5000 steps.  
The pressure distribution of the panel is shown in Figure 7. For the back areas of the side mirror, the area of the length of the side mirror represents negative pressure and the other following areas show positive pressure. Horseshoe vortices are generated on the panel in front of the side mirror, where the positive pressure reaches the maximum.  
Figure 8 shows the velocity vector of the \(Y=0\) plane. Compared to the incompressible computation, the compressible computation captures smaller eddies and makes finer velocity vectors. The eddy  
Figure 6: Compressible computing mesh generation.  
Figure 7: Pressure distribution of the side mirror and the panel.  
current behind the side mirror can be clearly observed. The velocity behind the side mirror is the lowest, and the velocity at the top of the side mirror is the highest. Then the velocity gradually returns to the normal value.  
The fluctuating pressure is generated on the side mirror and the panel and includes monopoles, dipoles and quadrupole sources simultaneously on the side mirror and the panel. Single and quadrupole sources are not considered here. The Curle dipole source is shown in Figure 9. The dipole source on the surface of the side mirror is the largest, and the sound source along both sides of the side mirror is also very large. The sound source on the panel presents a random distribution.