## 2 Construction of Numerical Calculation Model  
### Turbulence Mathematical Model and VOF Model  
The principal turbulence models are the Spalart model, the \(k\)-\(\varepsilon\) model, the Reynolds stress model, and the large eddy simulation (LES) model, among others. The Spalart model is primarily employed in the field of aeronautics for the simulation of wall-confined flows. The Reynolds stress model does not necessarily yield superior results to the \(k\)-\(\varepsilon\) model for general reflux flow. However, it is a computationally demanding approach that necessitates a high level of computational resources. The LES model is only applicable to three-dimensional problems, yet it is a highly computationally intensive model. In conclusion, the \(k\)-\(\varepsilon\) model has been selected for inclusion in this article. The aforementioned models comprise the standard \(k\)-\(\varepsilon\) model, the RNG \(k\)-\(\varepsilon\) model, and the realizable \(k\)-\(\varepsilon\) model. The RNG \(k\)-\(\varepsilon\) model and the realizable \(k\)-\(\varepsilon\) model demonstrate superior accuracy in comparison to the standard model. Given the complex layout of the subway station under study, comprising numerous columns, the RNG \(k\)-\(\varepsilon\) model was selected as the turbulence model for this research. In order to reduce the complexity of the model and the computational workload, the components of the subway station were simplified during the modelling process. For example, stairs were represented as sloping surfaces, as the primary focus of the article is not the flow of floodwater over stairs, and this simplification has a minimal impact. The transport equations for the RNG \(k\)-\(\varepsilon\) model are as follows:  
\[\frac{\partial}{\partial t}(\rho k)+\frac{\partial}{\partial x_{i}}(\rho ku_{ i})=\frac{\partial}{\partial x_{j}}\left(\alpha_{k}\mu_{eff}\frac{\partial k }{\partial x_{j}}\right)+G_{k}+G_{b}-\rho\varepsilon-Y_{M}+S_{k} \tag{1}\]  
\[\frac{\partial}{\partial t}(\rho\varepsilon)+\frac{\partial}{\partial x_{i} }(\rho\varepsilon u_{i})=\frac{\partial}{\partial x_{j}}\left(\alpha_{t}\mu_ {eff}\frac{\partial\varepsilon}{\partial x_{j}}\right)+C_{1\varepsilon} \frac{\varepsilon}{k}(G_{k}+C_{3\varepsilon}G_{b})-C_{2\varepsilon}\rho\frac {\varepsilon^{2}}{k}-R_{\varepsilon}+S_{\varepsilon} \tag{2}\]  
where \(G_{k}\) denotes the turbulent kinetic energy generation term due to the mean velocity gradient; \(G_{b}\) is the buoyancy-induced turbulent kinetic energy generation term; \(Y_{M}\) represents the contribution of the pulsating expansion to the total dissipation rate in compressible turbulence; \(\alpha_{k}\) and \(\alpha_{\varepsilon}\) are the inverse of the effective Prandtl number for \(k\) and \(\varepsilon\), respectively; and \(S_{k}\) and \(S_{\varepsilon}\) are user-defined source terms.  
A further objective of this article is to provide an accurate representation of the position of the flood liquid level, which is a fundamental aspect in determining the volume occupied by the flood. The volume of fluid (VOF) method is typically employed and is widely recognised for delineating interfaces between two or more immiscible fluids [26; 27; 28]. In the VOF model, the sum of the volume fractions for all fluids is equal to one. It thus follows that if the volume fraction of each fluid (phase) is denoted as \(\alpha_{q}\), it holds that \(\sum\alpha_{q}=1\). In this study, the model treats the fluids as two distinct phases, air and water, which are immiscible, constituting a gas-liquid two-phase flow. The VOF model provides an accurate determination of the liquid level position, expressed as \(\alpha_{w}+\alpha_{a}=1\).