Flux closures and source term models for shallow water models with depth-dependent integral porosity

Abstract

A two-dimensional shallow water model with depth-dependent porosity is presented. The purpose is the coarse grid simulation of shallow ows over complex topographies and geometries. Two ux closures are examined: the Integral Porosity (IP) and Dual Integral Porosity (DIP) closures. Energy losses are described using a subgrid scale model that accounts for bottom and wall friction, transient momentum dissipation and energy losses induced by obstacle submersion. A complete wave propagation property analysis is provided for the IP and DIP closures, yielding more accurate numerical stability constraints than published previously. Five computational examples are presented, including transients in compound and meandering channels, urban dambreak problems with building submersion and runo over variable microtopography. The ability of the model to deal with subgrid-scale features is conrmed. The DIP ux is shown to be superior to the IP closure. The transient dissipation term is essential in reproducing the eect of obstacles and microtopography. Distinguishing between the building wall-and building roof-induced friction is seen to be essential. The model is validated successfully against a scale model experimental dataset for the submersion of a coastal urban area by a tsunami wave.

Modelling urban floods using a finite element staggered scheme with an anisotropic dual porosity model

“…The model does not account for transient momentum dissipation due to shock wave reflections that occur when obstacles force a supercritical flow to change its direction (Guinot, 2012(Guinot, , 2017bGuinot et al, 2017Guinot et al, , 2018Viero et al, 2013b). This is consistent with the fact that the Finite Element model is not intended to deal with supercritical flows nor with shock waves.…”

Generalized Pareto processes for simulating space-time extreme events: an application to precipitation reanalyses

“…To help with this understanding, we develop a method to stochastically simulate realistic spatio-temporal extreme scenarios, which can be fed to impact models. Examples of impact models are urban flood models, such as the shallow water models of Guinot and Soares-Frazão (2006) and Guinot et al (2017), which produce hydrological variables such as water height or water speed, based upon which experts make decisions about flood risk.…”

Porosity Models for Large-Scale Urban Flood Modelling: A Review

“…Porosity parameters are defined either as statistical descriptors of the urban area at large-scale [10,20] or from local geometric features [9,11,21]; • Models include either a single [10,20] or multiple porosity parameters [9,11,[15][16][17]; • Effect of porosity in model fluxes and source terms is either isotropic [10,20] or anisotropic [9,11,12,15,16,[21][22][23]; • Porosity parameters are either depth-independent [9][10][11]17] or depth-dependent [12,22,23]; • Models are expressed in differential [10,20,21] or in integral form [9,11]; Moreover, the underlying flow model may correspond to the complete shallow-water equations (dynamic wave) [9][10][11][12]15,20,22,23] or to an approximation thereof, such as the diffusive wave [24][25][26]. Porosity as a statistical descri...…”