Single Porosity Model: Exploring the Spatial Resolution Limits in Complex Urban Patterns

When modeling large-scale urban floods, the use of porosity non-linear shallow water equations (PNSWE) emerges as an interesting sub-grid approach for reducing computation time while preserving the structure of the solution. In such models, fine-scale topographic information is represented at a coarser scale through porosity parameters, enabling a speed-up in computations at the expense of losing accuracy while computing hydrodynamic variables. Porosity accounts for both the change in storage and exchange section due to the presence of obstacles (e.g., houses or buildings) in the floodplain and introduces a new source term associated with its gradient into the momentum equations. Here, we use the Single Porosity model (SP) in Cartesian coordinates to simulate flows in both an idealized and a real-world urban area, while gradually increasing the spatial resolution. During such partial coarsening, in which we move from fine-to macro-scale, the porosity distribution changes within the urban zone from a highly heterogeneous field to a more uniform one. At an intermediate meso-scale, where the cell size is of the order of the street width and the reduction in computation time is still significant, the main preferential flow paths within the urban area can be captured by means of the porosity gradient. At such a scale, good agreement with refined classical model solutions is found for flow depth, flood extension, and hazard index, both in magnitude and spatial distribution. Numerical results highlight the importance of porosity models for quickly assessing flow properties during an event and improving real-time decision-making through reliable information