## 3 Methodology and Validity of CFD Simulations  
[PERSON] et al. conducted road tests on the buffeting noise of a sedan caused by different side window openings [11]. The results showed that Helmholtz resonance plays an important role. Flow over an open side window in a vehicle exhibits similar characteristics to the flow over an open deep cavity. They all present the phenomenon of flow-excited Helmholtz resonance. A deep cavity as a benchmark problem for the validity of the CFD simulations is shown in Figure 1.  
The dimensions are similar to those used in wind tunnel experiments. The methodology for obtaining these experimental results has been described in the literature [4; 17]. Flow is fully turbulent over the cavity with an inlet-free stream velocity of 25 m/s. One receiver point, at the center of the cavity bottom, is considered to validate the frequency spectrum with experimental results. To ensure an accurate resolution of the shear layer dynamics, more meshes are allocated over the opening of the cavity. The minimum grid spacing around the cavity corners is set to 0.1 mm. The total number of node points is approximately 2.576352 \(\times\) 10\({}^{6}\), and the number of hexahedral cells is 2.504167 \(\times\) 10\({}^{6}\). The total number of elements is 2.647365 \(\times\) 10\({}^{6}\). Partial grids along the longitudinal symmetry plane and prism layer are shown in Figure 2.  
To assess the reliability of the numerical solution, a grid dependence study was carried out, as shown in Table 1. The mean pressure coefficient and the peak values of the second monitor point's pressure fluctuation have been extracted from the simulation results for the three different mesh refinements. From Table 1, the discrepancies for the receiver location's mean pressure coefficient are very small. Furthermore, the difference between the peak pressure fluctuation for the fine and medium mesh is not large. Therefore, a fine mesh was used in this study. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Grid**} & \multirow{2}{*}{
\begin{tabular}{c} **Number of** \\ **Elements** \\ \end{tabular} } & \multicolumn{4}{c}{**Mesh Size (mm)**} & \multicolumn{4}{c}{**Mean Pressure**} & \multicolumn{2}{c}{**Peak Value of the**} \\  & & **\(\mathbf{x_{\min}}\)** & \(\mathbf{x_{\min}}\)** & \(\mathbf{y_{\min}}\)** & \(\mathbf{y_{\max}}\)** & \(\mathbf{z_{\min}}\)** & \(\mathbf{z_{\max}}\)** & **Coefficient** & **Pressure Fluctuation** \\ \hline Coarse & 1.844382 \(\times\) 10\({}^{6}\) & 2.60 & 19.12 & 4.06 & 10.21 & 1.00 & 20.60 & 0.05159 & 92.75 pa \\ Medium & 2.247365 \(\times\) 10\({}^{6}\) & 2.30 & 15.85 & 3.03 & 6.21 & 0.50 & 18.81 & 0.05165 & 87.31 pa \\ Fine & 2.647365 \(\times\) 10\({}^{6}\) & 2.00 & 10.21 & 2.42 & 4.82 & 0.10 & 15.27 & 0.05171 & 86.56 pa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean pressure coefficient and peak value of the pressure fluctuation for monitor point 2. Figure 1: Cavity model and receiver location. Figure 2: Partial grids along the longitudinal symmetry plane and prism layer. Five monitoring lines were selected in the flow direction (x) of the opening area of the cavity; the height of each line is 0.9 m, and the distances from the front edge of the opening of the cavity are 0.01 m, 0.03 m, 0.05 m, 0.07 m, and 0.09 m. The streamwise direction length of the opening of the cavity (\(l_{c}\) = 0.1 m) is used for dimensionless treatment. In the simulation, the mean streamwise velocity of the monitoring point is obtained through calculation. The comparison between the wind tunnel test results and the simulation results is shown in Figure 3. The abscissa adopts the ratio of the mean velocity (\(U_{\text{mean-x}}\)) to inlet velocity (\(U_{0}\) = 25 m/s) for dimensionless treatment, and the ordinate takes the ratio of height (z) in the vertical direction to the opening height of the cavity (\(10l_{c}\) = 0.15 m) for dimensionless treatment.