## 2 Construction of Numerical Calculation Model
### Model Meshing and Boundary Condition Setting  
The grid division area is the space within the subway station where fluid can exist (Figure 3). The blue arrow indicates the entrance of the model, while the red arrow indicates the exit of the model. The mesh is divided using poly-hexcore, which is less numerous and faster to compute than other mesh types. The article presents three distinct working conditions. In order to verify the independence of the meshes, calculations are carried out with the boundary conditions of Case 3 in order to test the results. In the verification process, a variety of cell numbers and grid shapes are employed for analysis. The flow rate at the tunnel exit was calculated when the floodwater invaded the subway station at \(t=1\) s, as illustrated in Table 1 and Figure 4. At this juncture, the fluid at the tunnel exit is air. As the number of grids increases, the results in the table demonstrate a progressive convergence towards a specific value. As the number of grids increases, the calculation becomes more accurate. Nevertheless, when the number of grids is excessive, the computational burden increases significantly, while the accuracy improvement is relatively modest. At this juncture, the mesh is exhibiting boundary effects. Accordingly, a grid of test 4 was selected for analysis in the article. Figure 3: Gridding of subway stations and detailed grids of entrances/exits A. (Fluid inlets are shown by blue arrows and fluid outlets are shown by red arrows. A grid of penned sections is shown in detail). Figure 2: Connection between platform level and hall level (Passage S1, S2 and S3). The article employs the VOF method to determine the location of the flood level by the finite element method. Also, a surface tension model is used, and the surface tension coefficient of water is set constant at 0.071 N/m. Turbulence simulation is carried out using the RNG \(k\)-\(\epsilon\) model. The mathematical model is solved by the SIMPLE method. In the context of boundary conditions, the specification of water level heights at inlets is categorised into three distinct types: water inlet, air inlet, and fluid outlet. A velocity inlet is specified on the input surface with a mean velocity for the water inlet, whereas other inlets and outlets are designated as pressure inlets and pressure outlets. As the inlet and outlet are directly connected to the external environment, the pressure inlet and pressure outlet are both at atmospheric pressure. The text makes the assumption that air is incompressible. If air were compressible, the cumulative volume of air within a subway station would increase, thereby raising the air pressure inside. Such a change would consequently impact the pressure level at the pressure inlet and, in turn, the velocity magnitude at the water inlet. Nevertheless, this is at odds with the simulation setup, which assumes air to be incompressible throughout. In flood simulations, an initial velocity is assumed to be present when water enters subway stations. The classification of water flow and air at the entrance results in a fluid volume fraction of 1 at the water inlet. While water inlets are used to specify flood heights, it is important to note that, in reality, flood heights rarely remain constant; they fluctuate. This discrepancy has an impact on the realism of the water levels. In order to ascertain the flow velocity of floods at the entrance, [PERSON] [29] constructed a 1:2 physical model of a subway station entrance staircase for experimental purposes. The relationship between the single-width flow rate of floodwater intrusion into \begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Number** & **Number of Grid Cells** & **Mass Flow Rate at Tunnel** \\  & **(\(\times 10^{6}\))** & **Exit (kg/s)** \\ \hline
1 & 0.2 & 98.26 \\
2 & 0.4 & 65.32 \\
3 & 0.9 & 60.13 \\
4 & 1.4 & 59.01 \\
5 & 1.7 & 57.99 \\
6 & 2.4 & 57.35 \\
7 & 2.8 & 56.30 \\
8 & 3.3 & 56.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tests for grid independence. Figure 4: Tests for grid independence.