A shallow-water model with depth-dependent porosity for urban flood modeling

The availability of high-resolution topographic data enables the modeling of urban floods with a high level of accuracy. However, such a modelling has a poor computational efficiency. Subgrid models enable to decrease the computational time by using coarse cells while preserving information from the detailed topographic data to some degree. In particular, shallow-water models with porosity constitute a subgrid model well-adapted for urban flood modeling. In this article, a new set of fully dynamic shallow-water equations with depth-dependent porosities is presented. Then, the implementation of the model is detailed and preliminary results obtained for a theoretical two-dimensional urban area are analyzed. Unlike recent works, the new model solves the fully dynamic shallow-water equations with depth-dependent and anisotropic porosities, a divergent formulation of the bed slope term, a non-staggered grid with quadrilateral cells and an efficient use of look-up tables to store the porosity relations.