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SUMMARYTwo-dimensional shallow water models with porosity appear as an interesting path for the large-scale modelling of oodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the oodplain. The introduction of a porosity into the two-dimensional shallow water equations leads to modiÿed expressions for the uxes and source terms. An extra source term appears in the momentum equation. This paper presents a discretization of the modiÿed uxes using a modiÿed HLL Riemann solver on unstructured grids. The source term arising from the gradients in the topography and in the porosity is treated in an upwind fashion so as to enhance the stability of the solution. The Riemann solver is tested against new analytical solutions with variable porosity. A new formulation is proposed for the macroscopic head loss in urban areas. An application example is presented, where the large scale model with porosity is compared to a reÿned ow model containing obstacles that represent a schematic urban area. The quality of the results illustrates the potential usefulness of porosity-based shallow water models for large scale oodplain simulations.

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