Floodwater pathways in urban areas: A method to compute porosity fields for anisotropic subgrid models in differential form

In the framework of porosity models for large-scale urban floods, this work presents a method to compute the spatial distribution of the porosity parameters of complex urban areas by analyzing the footprints of buildings and obstacles. Precisely, an algorithm is described that estimates the four parameters required by the differential, dual-porosity formulation we recently presented. In this formulation, beside the common isotropic porosity accounting for the reduced storage volume due to buildings, a cell-based conveyance porosity is introduced in the momentum equations in tensor form to model anisotropic resistances and alterations in the flow direction due to presence of preferential pathways such as streets. A cell-averaged description of the spatial connectivity in the urban medium and of the preferential flow directions is the main ingredient for robust and mesh-independent estimates. To achieve this goal, the algorithm here presented automatically extracts the spatially distributed porosity fields of urban layouts relying only on geometrical information, thus avoiding additional calibration effort. The proposed method is described with the aid of schematic applications and then tested by simulating the flooding of complex urban areas using structured Cartesian grids. A Fortran implementation of the algorithm is made available for free download and use.