A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations. (November 2017)

• Record Type: Journal Article
• Authors: Guinot, Vincent
• Is Part Of: Advances in water resources. Volume 109(2017)
• Page Start: 133
• Page End: 157
• Publication Date: 2017-11
• Subjects: Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2017.09.002
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: The flux and source term formulae for the Single Porosity (SP) Integral Porosity (IP) and Dual Integral Porosity (DIP) models are assessed using 96 refined flow simulations. The DIP mass and normal momentum flux closures outperform those of the IP and SP models. The existence of a momentum dissipation term active only in transient mode is confirmed. All transverse momentum flux closures fail for non-orthogonal street networks and/or wave propagation not aligned with the street network. All previously published SP, IP and DIP drag models are inaccurate. Abstract: The validity of flux and source term formulae used in shallow water models with porosity for urban flood 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 different geometries are considered. 18 two-dimensional initial value problems and 6 two-dimensional boundary value problems are defined. This results in a set of 96 fine grid simulations. Analysing the simulation results leads to the following conclusions: (i) the DIP flux 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 flux 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 confirms 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 flow configurations to be accounted for(vi) future laboratory experiments aiming at the validation of flux and source term closures should focus on the high-resolution, two-dimensional monitoring of both water depth and flow velocity fields.