Consistency and bicharacteristic analysis of integral porosity shallow water models. Explaining model oversensitivity to mesh design. (September 2017)

• Record Type: Journal Article
• Authors: Guinot, Vincent
• Is Part Of: Advances in water resources. Volume 107(2017)
• Page Start: 43
• Page End: 55
• Publication Date: 2017-09
• Subjects: Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2017.06.008
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: A consistency analysis of integral porosity shallow water models is carried out for triangular and quadrangular cells. The integral porosity formalism is shown to introduce artificial first- and null-order derivatives in the truncation error of the discretized equations. A bicharacteristic analysis of the governing equations allows the oversensitivity of model results to grid design to be explained. An alternative approach to point-based boundary porosity must be found for integral porosity models. Abstract: The Integral Porosity and Dual Integral Porosity two-dimensional shallow water models have been proposed recently as efficient upscaled models for urban floods. 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 fields induce an artificial polarization of the mass/momentum fluxes along preferential directions when triangular meshes are used and (iii) extra first-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 satisfied at all computational points when real-world situations are dealt with.