Shallow water equations with depth-dependent anisotropic porosity for subgrid-scale topography

This paper derives a novel formulation of the depth-averaged shallow water equations with anisotropic porosity for computational efficiency reasons. The aim is to run simulations on coarser grids while maintaining an acceptable accuracy through the introduction of porosity terms, which account for subgrid-scale effects. The porosity is divided into volumetric and areal porosities, which are assigned to the cell volume and the cell edges, respectively. The former represents the volume in the cell available to flow and the latter represents the area available to flow over an edge, hence introducing anisotropy. The porosity terms are variable in time in dependence of the water elevation in the cell and the cumulative distribution function of the unresolved bottom elevation. The main novelty of the equations is the formulation of the porosities which enables full inundation of the cell. The applicability of the equations is verified in five computational examples, dealing with dam break and rainfall-runoff simulations. Overall, good agreement between the model results and a high-resolution reference simulation has been achieved. The computational time decreased significantly: on average three orders of magnitude