Modelling urban floods using a finite element staggered scheme with an anisotropic dual porosity model

In porosity models for urban flooding, artificial porosity is used as a statistical descriptor of the urban medium. Buildings are treated as subgrid-scale features and, even with the use of relatively coarse grids, their effects on the flow are accounted for. Porosity models are attractive for large-scale applications due to limited computational demand with respect to solving the classical Shallow Water Equations on high-resolution grids. In the last decade, effective schemes have been developed that allowed accounting for a wealth of sub-grid processes; unfortunately, they are known to suffer from oversensitivity to mesh design in the case of anisotropic porosity fields, which are typical of urban layouts. In the present study, a dual porosity approach is implemented into a two-dimensional Finite Element numerical scheme that uses a staggered unstructured mesh. The presence of buildings is modelled using an isotropic porosity in the continuity equation, to account for the reduced water storage, and a tensor formulation for conveyance porosity in the momentum equations, to account for anisotropy and effective flow velocity. The element-by-element definition of porosities, and the use of a staggered grid in which triangular cells convey fluxes and continuity is balanced at grid nodes, allow avoiding undesired mesh-dependency. Tested against refined numerical solutions and data from a laboratory experiment, the model provided satisfactory results. Model limitations are discussed in view of applications to more complex, real urban layouts.