A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations

Abstract

To cite this version:Vincent Guinot. A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations. Advances in Water Resources, Elsevier, 2017, 109, pp.133-157 AbstractThe validity of ux and source term formulae used in shallow water models with porosity for urban ood simulations is assessed by solving the two-dimensional shallow water equations over computational domains representing periodic building layouts. The models under assessment are the Single Porosity (SP), the Integral Porosity (IP) and the Dual Integral Porosity (DIP) models. 9 dierent geometries are considered. 18 two-dimensional initial value problems and 6 two-dimensional boundary value problems are dened. This results in a set of 96 ne grid simulations. Analysing the simulation results leads to the following conclusions: (i) the DIP ux and source term models outperform those of the SP and IP models when the Riemann problem is aligned with the main street directions, (ii) all models give erroneous ux closures when is the Riemann problem is not aligned with one of the main street directions or when the main street directions are not orthogonal, (iii) the solution of the Riemann problem is self-similar in space-time when the street directions are orthogonal and the Riemann problem is aligned with one of them, (iv) a momentum balance conrms the existence of the transient momentum dissipation model presented in the DIP model, (v) none of the source term models presented so far in the literature allows all ow congurations to be accounted for(vi) future laboratory experiments aiming at the validation of ux and source term closures should focus on the high-resolution, two-dimensional monitoring of both water depth and ow velocity elds.

Numerical study of building drag dissipation for- mulations in the integral porosity shallow water model

“…1 (top). The second approach from literature is presented in [9]. The building drag dissipation is calculated as…”

“…The shallow water equations with porosity are most commonly used for flood simulations in urban areas, e.g. [1][2][3][4][5][6][7][8][9][10][11]. Another type of shallow water equations with porosity are applied to rainfall-runoff simulations in natural catchments, [12][13][14].…”

“…Several strategies to discretize the source term have been proposed in literature, such as isotropic formulations in [1,2,4,15] and anisotropic drag formulations in [7,17]. Current research agrees that anisotropic drag formulations should be preferred over isotropic ones [9,15,17]. The discretization of the drag dissipation source term is still an open issue.…”

“…In this paper, we introduce an anisotropic drag source term discretization technique, that is in its philosophy close to the one in [4]. Since all existing drag dissipation models are essentially wrong [9], our aim is to provide a simple yet useful anisotropic calculation of the drag dissipation source that avoids overparameterization.…”

“…First, we briefly present our mathematical models. Then, we compare this proposed formulation to the equations in [4] and [9] in a test case against measurement data and a high resolution shallow water model. Finally, we draw conclusions.…”