## 3 Methodology and Validity of CFD Simulations
It can be seen from Figure 3 that the trend of simulated values is consistent with the experimental values at different locations, and the shape of the mean velocity curve approximately matches with the inverse hyperbolic tangent function distribution, which is consistent with the literature [24]. This proves that the zonal SAS \(k\)-\(\varepsilon\) turbulence model can accurately capture the flow characteristics. Based on the time histories of the fluctuating pressure, it is possible to convert the computed data to the frequency-domain results by a standard fast Fourier transform (FFT) routine. The sound pressure level (\(SPL\)) was finally converted to dB units using the formula:  
\[SPL=20\log\frac{p}{p_{ref}} \tag{7}\]  
where \(p\) is the fluctuating pressure and \(p_{ref}\) is the sound pressure for reference:  
\[p_{ref}=2\times 10^{-5}\text{pa} \tag{8}\]  
Figure 4 displays the computed and measured sound pressure level at monitor point 2 for the inlet flow speed of 25 m/s. Four resonant frequencies--101.0 Hz, 202.2 Hz, 303.3 Hz, and 403.3 Hz--could be easily identified from the experimental data. For the simulation results, four resonant peaks--102.8 Hz, 204 Hz, 308 Hz, and 408 Hz--are also shown in Figure 3. The first resonant peak is the fundamental frequency of the flow instability over the cavity. For the frequency of the first peak \(SPL\), there is no significant difference between the experimental results and the simulation results; the difference is less than 2 Hz. The frequency of the second peak \(SPL\) captured differs from the experimental value by 2 Hz, within acceptable ranges. Both the frequencies of the third peak \(SPL\) and the fourth peak \(SPL\) are further and further away from the test values. The overall trend of the \(SPL\) spectra captured by the zonal SAS \(k-\varepsilon\) turbulence model almost perfectly matches with the experimental  
Figure 3: Mean streamwise velocity profile at the cavity opening. Note: circles represent experimental values and solid lines represent simulated values. values. The present model underestimates the amplitude of the high-order resonance and overestimates the frequency of the high-order resonance, which may be explained by the following. First, these were caused by the difference between the numerical simulations and the experimental measurements. It is very important to note in our numerical simulations that a uniform velocity profile with a turbulent intensity of 0.5% was assumed at the inlet boundary of the flow field. However, the turbulent boundary expected in the experimental measurements was generally not available. Second, the computation model used in the present study did not include the simulation of the background noise. Third, this might be due to the fact that the higher-order modes cause relatively weak oscillation in the present simulation. In general, the agreement between the compared results is very satisfactory, showing the ability of the zonal SAS \(k-\varepsilon\) model to predict the cavity noise. It indicates that this model can be used for window buffeting noise predictions at earlier stages of the program and verification of the design of the buffeting fix.