Multiple porosity shallow water models for macroscopic modelling of urban floods

A multiple porosity model is proposed for the macroscopic modelling of urban floods. The macroscopic flow field is described using different regions with distinct porosities, water depths and velocity fields. These regions can exchange mass and momentum based on water level difference. Street networks or alignments of buildings along preferential directions are accounted for by introducing anisotropic velocity distributions in some of the regions. Dead zones, storage yards in buildings and other stagnant areas are accounted for in the model. The mass and momentum exchange between the flow regions induce additional head loss terms. The proposed model can be formulated in differential form, thus making equation discretization method- and mesh-independent. Computational examples show that, although the representative elementary volume does not exist at the scale of an urban area, the proposed model can give reliable results compared to classical refined two-dimensional shallow water models, with a computational effort reduced by a factor 20–200 depending on the test case.