## 2 Numerical Methodology
### Computational Domain and Mesh  
Figure 2 shows the overview and cross-section of the computational domain. The computational domain is (550 m + 840 m + 550 m) \(\times\) 50 m \(\times\) 50 m in volume and consists of three parts: the two acceleration domains at both ends with a length of 550 m (148.6 \(H\)) and the housing for sound emission alleviation domain at the center with a length (\(L_{S}\)) of 840 m. The boundary conditions of the computational domain are defined as shown in Figure 2a. The bottom surface is ground and set as a no-slip solid wall, while the other five surfaces are atmospheric condition and set as outlets with zero pressure [26; 29]. The surfaces of the train body and the housing for sound emission alleviation are set as no-slip solid walls. The entire computational model uses a hybrid grid of tetrahedral unstructured grids and prismatic grids. In addition, the meshes on the train body and wall of the housing for sound emission alleviation are refined to improve the calculation accuracy. To avoid the mesh size effect, a grid independence study was conducted before the formal simulations. Two different meshes with different numbers of cells were divided into two groups: coarse meshes (24 million) and fine meshes (32 million). Figure 3 shows the representative results obtained with the two meshes. When a train travels through the enclosed housing for sound emission alleviation at a speed of 350 km/h, the peak-to-peak aerodynamic pressure at the measuring point located at S2 is 1900.6 Pa and 1849.1 Pa for the two meshes, respectively, and the difference is 2.7%; the mesh is independent of the simulation results. Therefore, the coarse mesh (24 million) is used as the calculation mesh in this paper. The time step is set as 0.002 s, which is smaller than the 0.0025 s used in [PERSON] et al. [30], and the 0.005 s used in [PERSON] et al. [31]. The FVM was selected to discretize the computational domain. The second-order upwind scheme was chosen to discretize the convection and diffusion terms. The second-order implicit scheme was chosen to discretize the time derivative. SIMPLE was chosen as the pressure velocity coupling treatment, which was used by [PERSON] and [PERSON] [32], and the convection term applied the second-order upwind  
Figure 1: Computational models and surface meshes. (**a**) Train model. (**b**) Enclosed housing for sound emission alleviation. form. The \(Re=4.4\times 10^{7}\), the y+ around the train surface is approximately 350 and the CFL number is 2. The calculation of each case needs 168 h using 20 \(\times\) 24 CPUs for parallel calculations. Figure 3: Pressure curves with different mesh resolutions. Figure 2: Overview and cross-section of the computational domain. (**a**) Overview of the computational domain. (**b**) Cross-section of the computational domain. The dynamic mesh technique is utilized to simulate the movement of the train model [33; 34; 35]. There are three dynamic mesh update methods in FLUENT: smoothing, layering, and remeshing. In the present study, the layering method is adopted to implement the moving train relative to the housing for sound emission alleviation. The computational domain is divided into a stationary region and a moving region, as shown in Figure 4. The train and its surroundings are in the moving region, in which the mesh moves with the train. The movement of the train and its surrounding mesh is defined by a profile file. The outside is a stationary region containing the housing for sound emission alleviation. When the train moves forward, the dynamic layering method adds layers of cells in the field behind the moving region and deletes those in front of the moving region. The two regions exchange flow field information through the interface.