## 3 Model Validation  
The accuracy of numerical simulation in this study was validated using field test data of aerodynamic pressure on the sound barrier in the Tianjin-Qinhuangdao Passenger Dedicated Line in China from the literature [31]. Employing the aforementioned numerical simulation method, the calculation models corresponding to the field test were established.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Working Conditions** & **Sound Barrier–Train Center Distance (m)** & **Nose Length (m)** \\ \hline
1 & 2.00 & 3.0, 4.5, 6.0, 7.5, 9.0 \\
2 & 2.50 & 3.0, 4.5, 6.0, 7.5, 9.0 \\
3 & 3.00 & 3.0, 4.5, 6.0, 7.5, 9.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation calculation working conditions.  
Figure 6: Overall model for steady-state calculations.  
Figure 7: Train and sound barrier location and measurement points.  
In this scenario, the CRH 380B high-speed train travels at a speed of 385 km/h, with a distance of 3.4 m between the sound barrier and the center of the train. The simulated peak pressure on the inner surface of the sound barrier was compared with the field test data, and the results are presented in Table 3. In both transient and steady calculation models, the absolute differences in pressure peak results for two measuring points between numerical simulation and field measurements are below 4%. When the steady-state calculated pressure data is converted from spatial variation to time variation, and compared with the transient pressure curve, as depicted in Figure 8, it becomes evident that the steady-state model and the transient model exhibit substantial consistency in the change of pressure with time. Particularly noteworthy is the close proximity of pressure peaks at the head and tail cars. Figure 9 shows the pressure cloud of the numerically validated simulation model as well as the pressure distribution. Figure 10 shows the time-varying curve of aerodynamic pressure in the in-situ testing. It can be observed that the time variation curve of pressure obtained by numerical simulation closely aligns with the in-situ test results, particularly for the head wave. The peak pressure of the head wave in the numerical simulation closely approximates that observed in the in-situ test. These results affirm that the calculation methods and parameters employed in this study can accurately replicate the actual pressure distribution on the sound barrier [32]. Further parametric analyses can be conducted utilizing the aforementioned CFD modeling method.  
Figure 8: Comparison of steady-state and transient aerodynamic pressure curves: (**a**) First measurement point “219-2”; (**b**) Second measurement point “230-5”.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Measuring Point**} & \multirow{2}{*}{**Measured Peak (Pa)**} & \multicolumn{2}{c}{**Steady-State Simulation**} & \multicolumn{2}{c}{**Transient Simulation**} \\ \cline{3-6}  & & **Peak** & **Relative** & **Peak** & **Relative** \\  & & **Pressure (Pa)** & **Error** & **Pressure (Pa)** & **Error** \\ \hline
219-2 & 759 & 737 & \(-2.9\%\) & 780 & 2.8\% \\
230-5 & 767 & 742 & \(-3.3\%\) & 786 & 2.5\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of in-situ test values and simulated values of aerodynamic pressure.