## 2 Numerical Methodology
### Numerical Method  
When passing through the enclosed housing for sound emission alleviation, the train disturbs the surrounding air and generates strong wind. In the housing for sound emission alleviation, the air is strongly confined by the walls of the housing for sound emission alleviation and the train body; therefore, the flow field is three-dimensional, unsteady, viscous, compressible and turbulent. In the present study, the RANS method proved effective in simulating the flow field around a moving train [36; 37; 38], and the  
Figure 4: Schematic diagram of the dynamic layering method.  
Figure 5: The speed strategy of the train model.  
RNG k-\(\epsilon\) turbulent model was used to simulate the flow field, similar to [PERSON] et al. [10], [PERSON] et al. [30] and [PERSON] et al. [39]. The number of iteration steps for each time step is preset to 50 steps [29,40,41,42], and the residual is set to \(10^{-6}\). This approach considers the influence of vortex factors and low Reynolds number effects in a turbulent flow and adds an extra term to the \(\epsilon\) equation of the standard k-\(\epsilon\) model to effectively improve the accuracy. The governing equations are presented as below [25,43]:  
Continuity Equation:  
\[\frac{\partial\rho}{\partial t}+\frac{\partial(\rho u_{i})}{\partial x_{i}}=0 \tag{1}\]  
Momentum Equation:  
\[\frac{\partial(\rho u_{i})}{\partial t}+\frac{\partial}{\partial x_{j}}(\rho u _{i}u_{j})=-\frac{\partial p}{\partial x_{i}}+\rho g\delta_{i2}+\frac{\partial }{\partial x_{j}}[\mu(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u _{j}}{\partial x_{i}}-\frac{2}{3}\delta_{ij}\frac{\partial u_{i}}{\partial x _{l}})]+\frac{\partial}{\partial x_{j}}(-\rho\overline{u^{\prime}_{i}u^{ \prime}_{j}}) \tag{2}\]  
where \(u\) and \(u^{\prime}\) refer to the mean velocity and the pulsating velocity, respectively; \(\rho\) represents the air density; \(p\) is the static pressure; \(-\rho\overline{u^{\prime}_{i}u^{\prime}_{j}}\) is the gradient of Reynolds stress, based on Boussinesq assumption:  
\[-\rho\overline{u^{\prime}_{i}u^{\prime}_{j}}=\mu_{t}(\frac{\partial u_{i}}{ \partial x_{j}}+\frac{\partial u_{j}}{\partial x_{i}})-\frac{2}{3}(\rho k+ \mu_{t}\frac{\partial u_{k}}{\partial x_{k}})\delta_{ij} \tag{3}\]  
where \(\mu_{t}\) is the turbulent viscosity coefficient, as a function of turbulent kinetic energy \(k\) and turbulent dissipation rate coefficient \(\epsilon\):  
\[\mu_{t}=C_{\mu}\frac{k^{2}}{\epsilon} \tag{4}\]  
The transport equation of the RNG \(k\)-\(\epsilon\) turbulence model is similar to the standard \(k\)-\(\epsilon\) model. Turbulent kinetic energy (\(k\)) equation and dissipation rate (\(\epsilon\)) equation are:  
\[\frac{\partial}{\partial t}(\rho k)+\frac{\partial}{\partial x_{i}}(\rho ku_ {i})=\frac{\partial}{\partial x_{j}}(\frac{\mu_{eff}}{\alpha_{k}}\frac{ \partial k}{\partial x_{j}})+G_{k}-\rho\epsilon-Y_{M} \tag{5}\]  
\[\frac{\partial}{\partial t}(\rho\epsilon)+\frac{\partial}{\partial x_{i}}( \rho\epsilon u_{i})=\frac{\partial}{\partial x_{j}}(\frac{\mu_{eff}}{\alpha_ {k}}\frac{\partial\epsilon}{\partial x_{j}})+C_{1\epsilon}\frac{\epsilon}{k }C_{k}-C_{2\epsilon}^{*}