Modelling urban floods using a finite element staggered scheme with porosity and anisotropic resistance

Artificial porosity models for urban flooding use porosity as a statistical descriptor for the presence of buildings, which are then treated as subgridscale features. Computational efficiency makes porosity models attractive for large-scale applications. These models are typically implemented in the framework of two-dimensional (2D) finite volume collocated schemes. The most effective schemes, falling under the category of Integral Porosity models, allow accounting for a wealth of sub-grid processes, but they are known to suffer from oversensitivity to mesh design in the case of anisotropic porosity fields. In the present exploratory study, a dual porosity approach is implemented into a staggered finite element numerical model. The free surface elevation is defined at grid nodes, where continuity equation is solved; fluxes are conveyed by triangular cells, which act as 2D-links between adjacent grid nodes. The presence of building is modelled using an isotropic porosity in the continuity equation to account for the reduced water storage, and an anisotropic conveyance porosity in the momentum equations to compute bottom shear stress. Both porosities are defined on an element-by-element basis, thus avoiding mesh-dependency. Although suffering a number of limitations, the model shows promising results.