Single porosity model: Exploring the spatial resolution limits in complex urban patterns

Abstract

When modeling large-scale urban floods, the Porosity Nonlinear Shallow Water Equations (PNSWE) emerge as an interesting and consistent subgrid approach to reduce computational time while preserving the solution structure, allowing for computational efficiency at the cost of some loss in the accuracy of the results. Porosity accounts for changes in storage and exchanges due to obstacles in urban areas, and it introduces an extra source term proportional to the porosity gradient into the momentum equations. However, no systematic analyses on the effects of grid size have been performed in real domains, when this model is used to represent fine-scale topographic information at a coarser scale. In this study, we analyze how accuracy is affected by gradually increasing grid resolution in a generalized porosity approach computed at the cell-level. The Single Porosity model (SP) in Cartesian coordinates is employed to simulate a real-world urban flooding event, with resolution transitioning from fine- to macro-scale. At an intermediate scale, the meso-scale, where cell size approximates street width and computational time is significantly reduced, the model captures main preferential flow paths by means of the porosity gradient within the urban area. Good agreement with refined classical model solutions is observed at this scale for flood extension and hazard maps, providing valuable information for early-warning systems. Numerical results underscore the importance of porosity models in rapidly assessing flow properties during an event, enhancing real-time decision-making with reliable information.