Flood inundation modeling in urbanized areas: A mesh-independent porosity approach with anisotropic friction

In the present work, a porosity-based numerical scheme for the Shallow Water Equations is presented. With the aim of accounting for the presence of storage areas, such as gardens, yards and dead zones, and for preferential flow pathways, both an isotropic storage porosity parameter and anisotropic friction are adopted. Particularly, the anisotropic effects due to the building alignments are evaluated defining conveyance porosities along principal directions and using them to express the friction losses in tensor form. The storage and conveyance porosities are evaluated from the geometry of the urban layout at a district scale and then assigned to computational cells rather than to cell sides, thus avoiding oversensitivity to the mesh design. The proposed formulation guarantees the C-property also in presence of wet-dry fronts. Model testing is performed analyzing schematic and idealized urban layouts, and against experimental data as well. The results obtained by the proposed anisotropic scheme are similar to a high-resolution model with resolved buildings, also in the presence of low-friction regimes, meanwhile with a remarkable reduction of the computational times.