Shallow water equations with binary porosity and their application to urban flooding

Abstract

Climate change and urbanization, among various factors, are expected to exacerbate the risk of flood disasters in urban areas. This prompts the construction of appropriate modeling tools capable of addressing full-scale urban floods for hazard and risk assessment. In this view, sub-grid porosity models based on the classic shallow water equations (SWE) appear to be a promising approach for full-scale applications in urban environments with reduced computational cost with respect to classic SWE models on high-resolution grids. The present work focuses on the recently proposed two-dimensional binary single porosity (BSP) model, which is a porosity flooding model written in differential form and based on the use of a binary indicator function to locate obstacles and buildings. Several applications (synthetic, experimental, and real-world cases) show that (i) the BSP results tend to the classic SWE solution for sufficiently refined mesh and that (ii) the BSP model can be successfully applied to realistic conditions with complicated terrain and obstacle distribution on coarser grids. Clearly, the adoption of medium/coarse grids makes the BSP model inherently less accurate than the classic SWE model on high-resolution grids, but the corresponding reduction of computational cost makes the use of the BSP model promising in full-scale urban flood applications when (i) multiple simulations are needed to perform stochastic or scenario analysis, (ii) no detailed information of local flow characteristics is required, and/or (iii) for complementing classic SWE models in a nesting cascade.