## 2 Numerical Simulation
### Turbulence Model  
Detached-eddy simulation (DES) is a turbulence simulation method that combines the Reynolds-Averaged Navier-Stokes (RANS) and large-eddy simulation (LES) methods. The RANS model is employed to accurately predict turbulence near the wall and within the boundary layer, capturing the intricate details of the flow. In regions further away from the wall, the LES model is employed to solve these issues for larger-scale turbulent structures. Nevertheless, DES has certain weaknesses, such as a reduction in modeled stress and the occurrence of grid separation. To address these vulnerabilities, an improved and extended version of DES called delayed detached-eddy simulation (DDES) was developed. DDES introduces a delayed transition from RANS to LES, allowing the RANS model to be effective in regions far from the wall [16]. Building upon DDES, the IDDES method further enhances simulation accuracy by using RANS in regions with a lower turbulence intensity and LES in regions with a higher turbulence intensity and LES.  
Figure 1: Schematic diagram of geometric models: (**a**) CRH3 train, (**b**) curved fence-type wind barrier, (**c**) front view of train-bridge-curved wind barrier system. (**d**) side view of train-bridge-curved wind barrier system (unit: m).  
well-defined dissipation. By employing the IDDES method, a more precise representation of turbulent flow characteristics can be achieved while reducing the computational resources required.  
Based on the shear stress transport \(k-\omega\) (SST \(k-\omega\)) turbulence model, the IDDES method is employed to investigate the characteristics of the sudden change in aerodynamic load of a HST induced by bridge wind barriers in crosswind environments, as well as the mitigation effect of buffer structures on these sudden changes. The SST \(k-\omega\) turbulence model is well-known for its accurate prediction of flow separation and is widely recognized as one of the most reliable turbulence models in engineering applications [17]. It is possible to estimate the length scale of IDDES by employing the following formula [18]:  
\[l_{hyb}=f_{hyb}(1+f_{e})l_{RANS}+(1-f_{hyb})l_{LES} \tag{1}\]  
\[l_{RANS}=\frac{\sqrt{k}}{C_{\mu}\omega},l_{LES}=C_{DES}\Delta \tag{2}\]  
\[f_{hyb}=\max\bigl{\{}(1-f_{dt}),f_{step}\bigr{\}} \tag{3}\]  
\[f_{dt}=1-\tanh[(20r_{dt})^{3}] \tag{4}\]  
\[r_{dt}=\frac{v_{t}}{\kappa^{2}d_{w}^{2}\sqrt{0.5(\mathbf{S}^{2}+\mathbf{ \Omega}^{2})}} \tag{5}\]  
where \(f_{hyb}\) is a mix function, \(f_{e}\) is known as the elevation function and is designed to prevent the excessive reduction of RANS Reynolds stresses. The scales of the RANS and LES regions are represented by \(l_{RANS}\) and \(l_{LES}\), respectively. \(k\) denotes the turbulent kinetic energy, \(\Delta\) is the LES length scale, and \(f_{step}\) is a function that provides a rapid switch from RANS to LES deep inside the boundary layer. \(f_{dt}\) is the delay function of DDES, \(v_{t}\) denotes the eddy viscosity, \(\kappa\) symbolizes the von Karman constant, \(d_{w}\) is the distance to the wall, and \(\mathbf{S}\) and \(\mathbf{\Omega}\) denote the normalized strain rate and rotation rate tensors in relation to the turbulence time scale, respectively.