## 3 Computational Configurations
### Computational Domain and Numerical Setup  
The computational model used in this paper is the pantograph placed on the train roof model with three cars to ensure the reasonability of the inflow and reduce the mesh amount. In addition, the computational domain is sufficiently large to eliminate the effects of the surrounding boundaries in the numerical simulation [36]. The origin of the used coordinate is at the bottom center of the train roof model and the inlet flow is due to the negative direction of \(x\)-axis. Moreover, the size of the computational domain is \(60\times 20\times 10\,\mathrm{H}\), where \(\mathrm{H}=2.85\,\mathrm{m}\), as depicted in Figure 5. To ensure that the inflow develops fully before reaching the head car, the upstream length is \(10\,\mathrm{H}\). Similarly, the downstream length is longer than \(20\,\mathrm{H}\) to ensure that the vortex shedding in the wake flow is well- developed. The computational domain is shown in Figure 6. This study mainly focuses on the effects of pantograph diversion strategies on train aerodynamic and aeroacoustic performance. Three configurations designed here, including the pantograph installed on the train roof alone, on the train roof sinking platform, and the pantograph fairing adopted on the train roof are described in Figure 7 and Table 2.  
Figure 7b illustrates the details of the sinking platform. For the sinking platform, its sinking height is \(0.15\,\mathrm{m}\), the width of front edge is \(2.1\,\mathrm{m}\), and the width of back edge is  
Figure 4: Computational model of pantograph. Figure 5: Side view of the computational model. Figure 6: Sketch of the computational domain. 0.9 m. The length of the sinking platform is 3.5 m in x direction. For the fairing, the specific parameters are clearly shown in Figure 7c as 8.3 and 2.3 m, respectively, and the largest height from the roof is 0.6 m, which is located at the rear edge of the sinking platform. To reduce the self-resistance, it remains streamlined at the front and back surface. To preclude the influence of grid, a grid independence study is carried out. Three grid resolutions including coarse, medium, and fine grids are set and the total drag coefficient of case 1 is compared, as shown in Table 3. It can be found that the calculated drag coefficient of case 1 shows a larger difference when the coarse and medium grids are adopted. In addition, the relative error in the calculated results between the medium and fine grid models is less than 2%. This indicates that the flow field computation results are reliable when the computational domain reaches the medium grid scale. The medium computational mesh is depicted in Figure 8. It is discretized by the poly-hexcore unstructured grid. The grid size of the pantograph surface is less than 8 mm to guarantee the prediction accuracy of the pantograph aerodynamic noise calculation. In addition, the boundary layer grids are generated near the pantograph surface, obtaining the first layer thickness of 0.12 mm which is normal to the wall, to ensure y+ \(\approx\) 1 with a growth ratio of 1.2. To capture the flow details, the refinement zone is carried out on the leeward side of the pantograph and the tail flow area of the roof model. The pressure far-field condition and the pressure outlet condition are prescribed for the inlet and outlet boundary here, respectively. Both side planes of the computational model and the top planes are set as symmetry boundaries. To simulate the ground effects, the ground is set to be the moving wall condition with an incoming velocity of 400 km/h. The physical time step of large eddy simulation is considered as \(5\times 10^{-5}\) s, and the corresponding aerodynamic noise for analysis frequency is 10 kHz, according to the Nyquist sampling theorem [37]. Moreover, 25 sub-steps are iterated within each time step and a total