## 2 Numerical Method
### Numerical Terrain Model
#### 2.4.3 Grids of the Terrain Model  
To ensure the numerical simulation accuracy of the terrain model grid, the grid independence checking was performed firstly. The mesh is divided into different parts. Unstructured prism was used to find grids near the ground, and the tetrahedral grid was adopted to reflect the undulating changes of the terrain. The near-wall grids of the terrain model are given in Figure 4. The detailed parameters of the three grids for independence checking are shown in Table 3. The computational domain and grid arrangement of the terrain model with BTS are shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Terrain Region** &
\begin{tabular}{c} **Geometry** \\ **Scale Ratio** \\ \end{tabular} & **Methods and Domain** & **Authors** \\ \hline
1 & 9.5 km \(\times\) 7.3 km & - & CFD & [PERSON], et al. [10] \\
2 & D = 15 km & 1:1000 & Wind tunnel test: 36 m (L) \(\times\) & [PERSON] et al. [29] \\
3 & D = 12 km & 1:1000 & Wind tunnel test: 25 m(L) \(\times\) & [PERSON] et al. [17] \\
4 & D = 5.0 km & 1:1500 & Wind tunnel test & [PERSON] et al. [27] \\
5 & D = 9.0 km & 1:1000 & CFD: 15 m (L) \(\times\) 15 m (B) \(\times\) & [PERSON], et al. [31] \\
6 & 15 km \(\times\) 14 km & - & CFD & [PERSON], et al. [26] \\
7 & D = 27.2 km & 1:4000 & Wind tunnel test: 14 m (L) \(\times\) & [PERSON], et al. [23] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of main parameters of mountainous terrain models. Figure 4: Computational domain, boundary conditions, and grid of terrain model without BTS. The flow solver used in this paper to simulate the wind characteristics over complex terrain is based on the finite-volume discretization in the space and the SIMPLEC (Semi implicit method for pressure linked equation consistent) pressure-correlation algorithm on a non-staggered grid arrangement ([PERSON], et al. [38]). The second-order cell-centered is adopted to deal with spatial discrete. The second-order upwind is used for time discrete. The time step is 0.015 s and the total amount of time steps is 10,000. According to the main parameters of wind-resistant design of the bridge, the mean cross-bridge wind speed and wind attack angles at the main deck level, longitudinal wind speed profiles at L/4, L/2 and 3L/4 of the bridge length were monitored to evaluate the calculation accuracy of different grids. The wind speed monitoring points are given in Figure 6.  
The grid sensibility was conducted by taking case 1 without BTS as an example. Numerical results of mean cross-bridge wind speed and wind attack angles of grid G1, G2, and G3 at the main deck level over the terrain model without BTS are given in Figure 7a,b, respectively. The longitudinal wind speed profiles at L/4, L/2 and 3L/4 of the bridge length of grid G1, G2, and G3 over the terrain model without BTS are shown in Figure 7c. It can be found in Figure 7a that the mean cross-bridge wind speed of G2 agrees well with that of G3 with a relative error of 23% while the result of G1 departs from the results of the other two grid generations to a great extent with relative error 116%. Note that the same tendency can be found in Figure 7b (relative error 41% for terrain model with BTS while 160% without  
Figure 5: Computational domain, boundary conditions and grid of terrain model with BTS. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Grid**} & **Mesh Size** & **Mesh Size in** & **Thickness of** & **Growth Rate of** & **Amount of** & **Total Mesh** \\  & **in Terrain** & **Computation** & **Boundary Layer** & **the Boundary** & **Layer Mesh** & **Layer** \\  & **Surface (m)** & **Domain (m)** & **Mesh (m)** & **High Boundary Layer** & **Total Mesh** \\ \hline G1 & 0.08 & 0.25 & 5 & 1.1 & 20 & 1,546,916 \\ G2 & 0.07 & 0.20 & 5 & 1.1 & 20 & 3,881,449 \\ G3 & 0.05 & 0.18 & 5 & 1.1 & 20 & 10,509,942 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Detailed setups of three grids of terrain model without BTS. Figure 6: Schematic diagram of monitoring points.