# Aerodynamic Analysis of the Opening Hood Structures at Exits of High-Speed Railway Tunnels
## 3 Methodology for Numerical Simulation
### Numerical Setups  
The simulations mentioned in this paper were performed using the commercial CFD solver ANSYS Fluent by solving the governing equations with the finite volume method. In typical scenarios, when a train enters and travels within a tunnel, the flow field characteristics in the vicinity of the train and inside the tunnel manifest a three-dimensional, unsteady, and turbulent state [20]. When the Mach number of the train's operating speed exceeds 0.3, the air is considered compressible. In this study, the train's speed is 400 km/h (111.11 m/s), which exceeds a Mach number of 0.3. Therefore, the compressibility of the air was considered in the subsequent simulations [21]. Compression waves radiate outward from the tunnel exit, leading to the generation of MPWs. These MPWs induce pressure discontinuities in the air surrounding the exit, subsequently causing airflow disturbances and generating aerodynamic noise. Currently, numerous studies have employed large-eddy simulation (LES) models to simulate aerodynamic noise and micro-pressure waves. Furthermore, the computed results have demonstrated favorable consistency with real-world data [22; 23; 24]. Therefore, in this study, the combination of three-dimensional, unsteady, compressible Navier-Stokes equations, and the LES model are chosen for simulating MPWs. The flow-solver type chosen for the simulation is the pressure-based solver. The coupled algorithm was selected to update the pressure-velocity coupling fields, while the Green-Gauss node-based method was used to control the gradients. The second-order upwind scheme was adopted for the density and energy equations, while the transient formulation was solved using a first-order implicit algorithm. The time step was set at \(5\times 10^{-4}\) s. For each time step, the maximum number of iterations is 50, and the residuals for all equations are set at 1 \(\times\)\(10^{-3}\)[24], which is consistent with Fluent's default convergence criteria. Given the complex geometry of the train's frontal section, an unstructured grid strategy is employed in this study to discretize the geometry model of the train's frontal part, while a structured grid strategy is adopted for the other part. When the train enters the tunnel and generates a compression wave, this wave propagates forward along the tunnel at the speed of sound. The airflow around the train body has a relatively minor influence on the propagation of compressional waves thanks to the significantly higher speed of sound compared to the velocity of the train. Therefore, volume cells are directly employed to  
Figure 2: Geometric model of train and tunnel: (**a**) high-speed railway tunnel; (**b**) front view of the train; and (**c**) side view of the train. discretize the area around the train in the simulation to conserve computational resources. This meshing strategy has been widely applied in simulating the aerodynamic effects of MPWs in high-speed railways [5; 25]. In the critical areas of the computational model, the grid size is refined with a minimum grid size of 0.05 m near the hood, train, and micro-pressure wave measurement points and a minimum grid size of 0.1 m in the tunnel area. The grid gradually becomes sparser at locations away from the critical areas, with a maximum grid size of 0.8 m. The computational domain grid is shown in Figure 3.  
In this study, the sliding mesh and dynamic mesh techniques provided by Fluent 15.0 software were employed to accurately simulate the relative motion between the train and the tunnel [26; 27; 28]. The computational domain was divided into two independent areas: the stationary area and the moving area. The stationary area comprises the left atmospheric domain, right atmospheric domain, and tunnel domain. The moving area consists of the train and the surrounding air, moving at the speed of the train during its operation. Information exchange between the two computational areas is achieved through an interface. The mountain near the entrances and exits of the tunnel is simplified as a vertical plane.