Shallow water equations with depth-dependent anisotropic porosity for subgrid-scale topography

Özgen, Ilhan; Liang, Dongfang; Hinkelmann, Reinhard

doi:10.1016/j.apm.2015.12.012

Cited by 35 publications

(41 citation statements)

References 47 publications

(89 reference statements)

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“…While the storage porosity does not include information on the anisotropy of the geometry, the connectivity porosity does because it is a function of the orientation of the boundary. The IP approach has been extended to depth-dependent porosity elds [34,35]. The Building Coverage Ratio/Conveyance Reduction Factor (BCR/CRF) approach [10,11] also uses two statistical indicators of the urban geometry that act in a similar fashion to that of the storage and conveyance porosities.…”

Section: Introductionmentioning

confidence: 99%

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

Guinot

Delenne

Rousseau

et al. 2018

Advances in Water Resources

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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.

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Section: Introductionmentioning

confidence: 99%

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

Guinot

Delenne

Rousseau

et al. 2018

Advances in Water Resources

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“…Distinguishing between a storage porosity (isotropic) and a conveyance porosity (anisotropic) allows for a better description of the ow eld than in the SP model [18,19]. A depth-dependent version has appeared recently [29,30]. The connectivity porosity, that is supposed 1 to account for building obstruction to the ow, should be smaller than the storage porosity, otherwise yielding wave propagation speeds articially larger than those in free water [13], an unphysical behaviour.…”

Section: Introductionmentioning

confidence: 99%

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

Guinot

2017

Advances in Water Resources

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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.

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Hinkelmann, R. (2016). Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity.

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confidence: 99%

Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity

Özgen

Zhao

Liang

et al. 2016

Journal of Hydrology

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Hinkelmann, R. (2016). Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity. Journal of Hydrology, 541, 1165Hydrology, 541, -1184Hydrology, 541, . https://doi.org/10.1016Hydrology, 541, /j.jhydrol.2016 Özgen, I.; Zhao, J.; Liang, D.; Hinkelmann, R.Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity The shallow water model with anisotropic porosity conceptually takes into account the unresolved subgrid-scale features, e.g. microtopography or buildings. This enables computationally efficient simulations that can be run on coarser grids, whereas reasonable accuracy is maintained via the introduction of porosity. This article presents a novel numerical model for the depth-averaged equations with anisotropic porosity. The porosity is calculated using the probability mass function of the subgrid-scale features in each cell and updated in each time step. The model is tested in a one-dimensional theoretical benchmark before being evaluated against measurements and high-resolution predictions in three case studies: a dam-break over a triangular bottom sill, a dam-break through an idealized city and a rainfall-runoff event in an idealized urban catchment. The physical processes could be approximated relatively well with the anisotropic porosity shallow water model. The computational resolution influences the porosities calculated at the cell edges and therefore has a large influence on the quality of the solution. The computational time decreased significantly, on average three orders of magnitude, in comparison to the classical high-resolution shallow water model simulation.

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Shallow water equations with depth-dependent anisotropic porosity for subgrid-scale topography

Cited by 35 publications

References 47 publications

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

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

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

Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity

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