# Formation Mechanism and Response Strategies for Urban Waterlogging: A Comprehensive Review
## 3 Analytical Framework
### Numerical Simulation
#### 3.3.1 Hydrodynamic Models  
Hydrodynamic models are mathematical tools that describe the flow characteristics and behavior of water bodies, primarily used to simulate the spatiotemporal distribution of flood flow, velocity, and water depth. Depending on the dimensionality and complexity, hydrodynamic models can be categorized into one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) models.  
One-dimensional models are the earliest type used for flood simulation, primarily based on the Saint-Venant equations to describe water flow along river channels. One-dimensional models are suitable for modeling flow in river networks [62]. [PERSON] et al. [75] proposed an improved 1D nonlinear dynamic model, finding that the approximation provided by the 1D model significantly deviates from the actual flow field. One-dimensional models are suitable for long-distance simulations of large water systems but perform inadequately in capturing lateral flow and local turbulence characteristics. This limitation motivated the adoption of 2D/3D frameworks, calibrated using experimental LSPIV velocity datasets to enhance local turbulence prediction.  
Two-dimensional models describe the planar motion of water flow by solving the shallow water equations, allowing for better representation of flood propagation characteristics in plains or urban areas. They are commonly used for studying urban flooding and effectively simulate changes in flow and water depth during inundation events. For instance, [PERSON] et al. [8] used an improved anisotropic porosity model to analyze the impact of urban morphological features on flood flow, revealing a significant correlation between urban characteristics and flood depth. [PERSON] et al. [76] employed a two-dimensional depth-averaged model to simulate urban flooding in Marseille and Ulin, concluding that the spatial distribution of rainfall input significantly affects water depth.  
Three-dimensional models (3D) extend into the vertical direction, simulating the three-dimensional movement characteristics of water flow by solving the Navier-Stokes equations. Three-dimensional hydrodynamic models have also been applied to more complex urban flow conditions. For example, [PERSON] et al. [75] compared 1D and 3D numerical models to analyze flow characteristics at the junctions of open channels, finding that traditional 1D models may not accurately reproduce flow field characteristics in certain cases, and parameterizing 3D features can enhance the accuracy of large-scale water network models. Different types of models and related studies are shown in Table 2.  
Using models in isolation has its limitations [79]. Thus, the combined application of different models can leverage the advantages of each dimension model, such as coupling 1D and 2D models. [PERSON] et al. [47] employed a dynamic bidirectional coupled model, integrating 1D-2D hydrodynamic and water quality simulations to explore the formation process of urban waterlogging in Changzhi City, China. [PERSON] et al. [77] proposed a dynamic 1D-2D coupled model to simulate urban flooding, with results indicating that the physically-based 2D overflow diffusion model outperforms geological statistical models, suggesting their combined use. [PERSON] et al. [80] investigated the application of Structure from Motion (SfM) photogrammetry technology for high-resolution topographic surveys in urban drainage physical models to simulate runoff under different rainfall intensities, with results showing that the 2D model using SfM topographic data outperformed traditional measurement methods in replicating experimental data.