## 2 Numerical Model  
### Maglev Train and Tunnel Model  
In this study, a 600-km/h magnetic levitation test train was developed in China as the object of study. The train model was scaled down to 1:20 prior to the numerical simulation because the full y+ wall treatment was used and the y+ needed to be controlled to be less than 1 or greater than 30. Figure 1 illustrates the training model. At full scale, the maglev train has a height of h = 4.14 m, cross-sectional area of 11.95 m\({}^{2}\), T-shaped track beam with a track surface of 1.09 m from the ground, and a bottom surface at 0.3 m from the ground. Using the maglev train height as a benchmark for data in this study for dimensionless processing, the car length is 20.1 h, car width is 0.89 h, head car is 7.04 h, middle car is 5.97 h, and nose height is 0.34 h. The entire car is composed of four parts: frame, wheel assembly, outer shell of the rolling stock, and an on-board test system [20]. Figure 1: Maglev train model. Owing to the extremely strict requirements of the equipment form factor at the tunnel limit, the arrangement of the equipment inside the tunnel should be compact. Therefore, it is particularly important to reduce the neck length and influence the flow field while expanding the spectral range of the resonator [21]. [PERSON] et al. [22] examined that the Helmholtz resonator neck can be extended inward to reduce the resonant frequency while maintaining its surface finish. In summary, all the Helmholtz resonators in this study were single-cavity double-necked, with an inward extending neck, a neck hole diameter length of d = 0.14 h, and a neck channel depth of l = 0.1 h (as shown in Figure 2). In the experiments in this study, a number of different Helmholtz resonator arrangements with 94, 72, and 64 cavities were set up as follows:  
1. Conventional tunnel without Helmholtz resonators and without any additional structures. 2. A 94-cavity new tunnel comprising 94 cavities arranged continuously without intervals on both sides of the tunnel, starting at 4.78 h from the entrance and ending at 6.83 h from the exit of the tunnel. 3. A 72-cavity new tunnel 1, the 72 cavities were divided into 24 groups, each group consisting of 3 cavities, with an interval of 1.76 h between each group, starting inside the tunnel at 4.78 h from the entrance and ending at 6.83 h from the tunnel exit. 4. A 64-cavity new tunnel, the 64 cavities were divided into 32 groups, each group consisting of 2 cavities, with an interval of 1.76 h between each group, starting inside the tunnel at 2.39 h from the entrance and ending at 6.83 h from the tunnel exit. 5. A 72-cavity new tunnel 2, the 72 cavities were divided into 24 groups, each group consisting of 3 cavities, with an interval of 1 h between each group, arranged from 2.39 h inside the tunnel from the entrance and ending at 15.18 h from the exit of the tunnel. The specific programmer is listed in Table 1.  
When multiple Helmholtz resonators are used, the distance between the necks of the chambers must be considered. When the distance between the different cavity necks is \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Conventional** & **94-Cavity New Tunnel** & **72-Cavity New Tunnel 1** & **64-Cavity New Tunnel** & **72-Cavity New** \\ \hline Number of Cavities & 0 & 94 & 72 & 64 & 72 \\ Distance from entrance & 0 & 4.78 h & 4.78 h & 2.39 h & 2.39 h \\ Distance to exit & 0 & 6.83 h & 6.83 h & 6.83 h & 15.18 h \\ Distance between two cavities & 0 & 0 & 1.76 h & 1.76 h & 1 h \\ Layout location & 0 & Bottom of both sides & Bottom of both sides & Bottom of both sides & Bottom of both sides \\  & & & & & \\  & & & & & \\  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Helmholtz resonator module arrangement. Figure 2: Helmholtz resonator. (**a**) Helmholtz resonators 3D simulation; (**b**) Helmholtz resonator structure. too small or the cavity itself is too small, the effect of the Helmholtz resonators will be limited by each other. This reduces the relief effect as opposed to increasing it.