## 2 Computational Methods and Model
### Target Model and Details on Simulation  
The target train model is EMU-320 (electric multiple unit--320) which is just about to start running as the next Korean high-speed train based on the HEMU-430X (high-speed electric multiple unit--430 km/h eXperiment) of which the design was unveiled in 2012 and for which the maximum speed was recorded as 430 km/h. However, for economical computational cost, but without losing the main aeroacoustic source mechanisms, only four coaches, named TC, M1, M'3, and TC2 cars, are considered in the current study. The overall side-view of the EMU-320 is shown in the upper part of Figure 3. The detailed geometries of the pantograph, HVAC, bogie, and inter-coach reported to be crucial aerodynamic noise sources, are depicted in of Figure 3b. The modeled train consists of eight bogies, two pantographs, and six HVAC systems. Outer windshields fully shield Inter-coach spaces of EMU320 While the train is running, the front pantograph goes down, and the rear pantograph goes up.  
Figure 2: Illustrative slanted Dirac cone separating incompressible and compressible parts in the three-dimensional periodogram: \(U_{0}=300\) km/h and \(c_{0}=343\) m/s.  
Figure 4 presents the two computational domains used to model the flow field around the EMU320 in the open field and the tunnel, respectively, with applied boundary conditions and related dimensions. The blockage ratio of the computation domain for the open-field case is 0.81%, which is much less than the typically accepted range of 5% according to CEN (European Committee for Standardization) [22]. The cross-sectional shape of the tunnel is determined by using the existing tunnel with a radius and area of 6.519 m and 98.81 m\({}^{2}\), respectively. The blockage ratio of the train cross-section to the tunnel cross-section is 0.111. The exact values of the applied boundary conditions are summarized in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Boundary Type** & **Setting** & **Remarks** \\ \hline O/T & Inlet boundary & Velocity inlet & 83.33 m/s, non-reflecting \\ O/T & Outlet boundary & Pressure outlet & 101,325 Pa, non-reflecting \\ O/ & Side and upper boundary & Pressure far field & 101,325 Pa, Ma = 0.24 \\ /T & Tunnel wall & Moving wall & 83.33 m/s \\ O/T & Ground & Moving wall & 83.33 m/s \\ O/T & EMU surfaces & No-slip wall & \\ O/T & Rail & Moving wall & 83.33 m/s \\ \hline \hline \end{tabular}
\end{table}
Table 3: Details on boundary setting for open field(O) and tunnel(T) cases.  
Figure 3: (**a**) Target train of EMU320 and (**b**) its detailed parts modeled.  
Figure 5 shows the grid descriptions for the main parts and the entire computational domains. The entire computation domains for open field and tunnel cases consist of about 590- and 625-million cells, respectively, which were constructed using fluent meshing (version: 18.0). The total number of cells used in the present study was increased by two times compared to the previous study [15]. Tetrahedral cells were used and five layers of prismatic elements have been generated just adjacent to the wall surface. The maximum grid size around the train surface did not exceed 10 mm, which allows for resolving an acoustic wave of the maximum target frequency of 2500 Hz with a minimum of 13 points per one wavelength. The time interval \(\Delta\)t was set to 2 \(\times\) 10\({}^{-4}\) s for a sampling frequency of 5000 Hz. To check the convergence of the calculations, the time-history of the total drag coefficient was monitored, as was done in [15]. The time data for the analysis was recorded for 0.2 s after 0.930 s and 1.026 s for the open-field and the tunnel cases, respectively.  
Figure 4: Computational domain and boundary conditions: (**a**) open-field case; (**b**) tunnel case.  
Figure 5: Computational gird descriptions: (**a**) surface meshes of its main parts, (**b**) volume meshes of open-field case in x-z plane and (**c**) volume meshes of tunnel case in the x-y plane.