基于建筑密度系数的二维城市洪水数值模拟

城市密集建筑群的存在对城市洪水演进有很大影响,而根据建筑物的尺寸和高程采用高分辨率网格进行逐渐构建的方法在大范围洪水数值模拟中有一定的局限性。因此,如何高效模拟出建筑群在洪水中的影响对城市洪灾风险评估至关重要。在浅水方程中引入了建筑密度系数以反映建筑群对城市洪水运动的影响,并建立二维城市洪水数值模型。模型采用中心迎风格式计算界面通量,并对界面两侧变量进行线性重构,使其在空间上有二阶精度。为保证模型的和谐性和稳定性,底床坡度项采用中心差分法离散,底床摩擦项和局部水头损失项用半隐式法离散。当库朗特数满足条件时,模型能保证计算水深在任何时刻是非负的。算例分析表明,模型在计算中可以将建筑群区域视为一个整体,受网格疏密制约较小。在计算精度相近的情况下,计算需时约为高分辨率网格法的1/50,能够简便、高效地模拟洪水在城市建筑群中演进的过程。

A Two-dimensional Numerical Model of Urban Flood Based on Building Density Coefficient

Dense buildings in modern city usually have a great influence on urban flood propagation,and the use of high resolution meshes to distinguish the buildings based on their actual size and elevation in large-scale urban flood simulation is often limited by the computational time.It is important to efficiently simulate the effect of buildings on flood propagation in the risk assessment of urban flood.In this paper,a two-dimensional numerical model of urban flood is established by introducing the Building Density Coefficient (BDC)in the shallow water equation to reflect the influence of buildings on the urban flood propagation.In the model,a central-upwind scheme is used to calcu-late the flux across the interface of computational mesh and the linear reconstruction of flow variables is adopted to achieve the second-order accuracy in space.A central difference method is used to discretize the bed slope source term to maintain the well-balanced property.The friction source term and local head loss term are calculated using a semi-implicit method to ensure the stability of model.The model can guarantee the positivity of water depth when the Courant number meets certain condition,which means there is no need to treat negative water depth problem. The simulated result shows that the established numerical model with BDC can deal with the building area as a whole zone and is not restricted by the grid size,which greatly shortens the computational time to 1 /50 of that using high resolution method with good accuracy.