Consistency and bicharacteristic analysis of integral porosity shallow water models. Explaining model oversensitivity to mesh design

The Integral Porosity and Dual Integral Porosity two-dimensional shallow water models have been proposed recently as e cient upscaled models for urban oods. Very little is known so far about their consistency and wave propagation properties. Simple numerical experiments show that both models are unusually sensitive to the computational grid. In the present paper, a two-dimensional consistency and characteristic analysis is carried out for these two models. The following results are obtained: (i) the models are almost insensitive to grid design when the porosity is isotropic, (ii) anisotropic porosity elds induce an arti cial polarization of the mass/momentum uxes along preferential directions when triangular meshes are used and (iii) extra rst-order derivatives appear in the governing equations when regular, quadrangular cells are used. The hyperbolic system is thus mesh-dependent, and with it the wave propagation properties of the model solutions. Criteria are derived to make the solution less mesh-dependent, but it is not certain that these criteria can be satis ed at all computational points when real-world situations are dealt with.