## 2 Computational Model of External Flow Field
### Numerical Model  
Figure 1 shows the geometric model of the high-speed maglev train. The maglev train is a five-car marshalling model with a scale of 1:8. Figure 2 shows the computational domain. The cross section of the low vacuum tube is fan-shaped with an area of 80 m\({}^{2}\). In order to ensure the stability of the computation in the low vacuum tube (that is, to suppress the numerical oscillation in the vacuum tube), in the longitudinal direction, the distance from the front end of the maglev train to the entrance boundary is 200 m, and the distance from the rear end of the maglev train to the exit boundary is 500 m. In the transverse direction, the entire computational domain is symmetric along the longitudinal symmetry plane of the maglev train. The front inlet of the computational domain is set as the pressure far field (given incoming flow Mach number) and non-reflective boundary conditions, the back end of the computational domain is set as the pressure outlet and non-reflective boundary conditions, the track and low vacuum tube are set as the sliding walls boundary conditions, the speed is consistent with the incoming flow speed, and the high-speed maglev train is set as the fixed wall. Commercial software, ICEM, is used for meshing, and the refined tetrahedral/triangular prism meshing is carried out through topology optimization, multi-layer mesh encryption technology, boundary layer mesh technology, and mesh stretching technology. The maximum mesh size of the streamlined parts of the head and tail cars is 30 mm, the maximum mesh size of the body parts of the head and tail cars is 40 mm, and the maximum mesh size of the middle car is 60 mm. Three encryption zones are set up around the high-speed maglev train. The maximum sizes of the encryption zone are 20 mm, 40 mm, and 60 mm, respectively. The streamlined part of the tail car is individually encrypted, and the maximum mesh size is 10 mm. The boundary layer mesh is set on the surface of the high-speed maglev train. The number of boundary layers is 8, and the total thickness is 0.3 mm. The number of computational meshes is more than 100 million. Figure 3 shows the computational mesh. The steady flow field is computed firstly, then the unsteady flow field is computed. For steady computation, the SST k-\(\upomega\) turbulence model is adopted for the turbulence simulation, the semi-implicit method for pressure-linked equations (SIMPLE) algorithm  
Figure 1: High-speed maglev model. Figure 3: Computational mesh: (**a**) Cross-section mesh, (**b**) boundary layer mesh. Figure 2: Computational model. is adopted for solving the pressure-velocity coupling, the standard scheme is used for discretizing the pressure equation, and the second upwind scheme is used for discretizing the momentum equation, turbulent kinetic energy equation, and turbulent dissipation equation. For unsteadiness computation, the steady flow field is set as the initial flow field, the LES method is adopted for the turbulent simulation, and the sub-grid model is the Smagorinsky model. The coupled algorithm is adopted for solving the pressure-velocity coupling. The unsteady calculation time step is \(5\times 10^{-5}\) s, and a total of 10,000 time-steps are computed. Figure 4 shows the y\({}^{+}\) on the train surface. As shown in Figure 4, the y\({}^{+}\) on the majority of the train surface region is less than 1, which could meet the computational requirement of the LES method. The computational model is verified by comparing the computational results of the pressure on the train surface with the wind tunnel test results. The wind tunnel test model is a three-car marshalling model with a scale of 1:8. The computational model for the model verification is consistent with the wind tunnel test model, and the mesh division method and the computational setting are consistent with those in Section 2.3. Figure 5 shows the comparison between the computational results of the pressure coefficient on the longitudinal symmetry line of the train and the wind tunnel test results.