skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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.

Authors:
 [1];  [1];  [2];  [1]
  1. Technische Univ. Berlin (Germany). Chair of Water Resources Management and Modeling of Hydrosystems
  2. Univ. of Cambridge (United Kingdom). Dept. of Engineering
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1482512
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Hydrology
Additional Journal Information:
Journal Volume: 541; Journal Issue: PB; Journal ID: ISSN 0022-1694
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; porous shallow water equations; anisotropic porosity; finite volume method; case studies

Citation Formats

Özgen, Ilhan, Zhao, Jiaheng, Liang, Dongfang, and Hinkelmann, Reinhard. Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity. United States: N. p., 2016. Web. https://doi.org/10.1016/j.jhydrol.2016.08.025.
Özgen, Ilhan, Zhao, Jiaheng, Liang, Dongfang, & Hinkelmann, Reinhard. Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity. United States. https://doi.org/10.1016/j.jhydrol.2016.08.025
Özgen, Ilhan, Zhao, Jiaheng, Liang, Dongfang, and Hinkelmann, Reinhard. Sat . "Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity". United States. https://doi.org/10.1016/j.jhydrol.2016.08.025. https://www.osti.gov/servlets/purl/1482512.
@article{osti_1482512,
title = {Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity},
author = {Özgen, Ilhan and Zhao, Jiaheng and Liang, Dongfang and Hinkelmann, Reinhard},
abstractNote = {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.},
doi = {10.1016/j.jhydrol.2016.08.025},
journal = {Journal of Hydrology},
number = PB,
volume = 541,
place = {United States},
year = {2016},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
journal, January 2004

  • Audusse, Emmanuel; Bouchut, François; Bristeau, Marie-Odile
  • SIAM Journal on Scientific Computing, Vol. 25, Issue 6
  • DOI: 10.1137/S1064827503431090

Scale issues in hydrological modelling: A review
journal, April 1995


Two-dimensional shallow flow equations for partially dry areas
journal, November 2000


Detailed data is welcome, but with a pinch of salt: Accuracy, precision, and uncertainty in flood inundation modeling: OPINION
journal, September 2013

  • Dottori, F.; Di Baldassarre, G.; Todini, E.
  • Water Resources Research, Vol. 49, Issue 9
  • DOI: 10.1002/wrcr.20406

Effects of Rainfall, Vegetation, and Microtopography on Infiltration and Runoff
journal, September 1991

  • Dunne, Thomas; Zhang, Weihua; Aubry, Brian F.
  • Water Resources Research, Vol. 27, Issue 9
  • DOI: 10.1029/91WR01585

Urban water interfaces
journal, June 2014


Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
journal, September 2009

  • Geuzaine, Christophe; Remacle, Jean-François
  • International Journal for Numerical Methods in Engineering, Vol. 79, Issue 11
  • DOI: 10.1002/nme.2579

Total variation diminishing Runge-Kutta schemes
journal, January 1998

  • Gottlieb, Sigal; Shu, Chi-Wang
  • Mathematics of Computation of the American Mathematical Society, Vol. 67, Issue 221
  • DOI: 10.1090/S0025-5718-98-00913-2

Data and hydroinformatics: new possibilities and challenges
journal, July 2009


Multiple porosity shallow water models for macroscopic modelling of urban floods
journal, March 2012


Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids
journal, January 2005

  • Guinot, Vincent; Soares-Frazão, Sandra
  • International Journal for Numerical Methods in Fluids, Vol. 50, Issue 3
  • DOI: 10.1002/fld.1059

Citywide multi-grid urban flood modelling: the July 2012 flood in Beijing
journal, November 2013


Improved total variation diminishing schemes for advection simulation on arbitrary grids: IMPROVED TVD SCHEMES FOR AS ON ARBITRARY GRIDS
journal, November 2011

  • Hou, J.; Simons, F.; Hinkelmann, R.
  • International Journal for Numerical Methods in Fluids, Vol. 70, Issue 3
  • DOI: 10.1002/fld.2700

A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment
journal, February 2013


RKDG2 shallow-water solver on non-uniform grids with local time steps: Application to 1D and 2D hydrodynamics
journal, February 2015


Mesh type tradeoffs in 2D hydrodynamic modeling of flooding with a Godunov-based flow solver
journal, June 2014


Urban flood modeling with porous shallow-water equations: A case study of model errors in the presence of anisotropic porosity
journal, April 2015


An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes
journal, December 2014


GPU implementation of the 2D shallow water equations for the simulation of rainfall/runoff events
journal, March 2015

  • Lacasta, Asier; Morales-Hernández, Mario; Murillo, Javier
  • Environmental Earth Sciences, Vol. 74, Issue 11
  • DOI: 10.1007/s12665-015-4215-z

Flood Simulation Using a Well-Balanced Shallow Flow Model
journal, September 2010


Adaptive quadtree simulation of shallow flows with wet–dry fronts over complex topography
journal, February 2009


Coupling surface and subsurface flows in a depth averaged flood wave model
journal, April 2007


Shallow water simulation of overland flows in idealised catchments
journal, August 2015

  • Liang, Dongfang; Özgen, Ilhan; Hinkelmann, Reinhard
  • Environmental Earth Sciences, Vol. 74, Issue 11
  • DOI: 10.1007/s12665-015-4744-5

Reduced complexity strategies for modelling urban floodplain inundation
journal, October 2007


Modeling floods in a dense urban area using 2D shallow water equations
journal, July 2006


Comparison of roughness models to simulate overland flow and tracer transport experiments under simulated rainfall at plot scale
journal, May 2011


The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes
journal, January 2007

  • Murillo, J.; García-Navarro, P.; Burguete, J.
  • International Journal for Numerical Methods in Fluids, Vol. 54, Issue 5
  • DOI: 10.1002/fld.1417

Drag, turbulence, and diffusion in flow through emergent vegetation
journal, February 1999


Shallow water equations with depth-dependent anisotropic porosity for subgrid-scale topography
journal, September 2016

  • Özgen, Ilhan; Liang, Dongfang; Hinkelmann, Reinhard
  • Applied Mathematical Modelling, Vol. 40, Issue 17-18
  • DOI: 10.1016/j.apm.2015.12.012

Upscaling the shallow water model with a novel roughness formulation
journal, August 2015

  • Özgen, Ilhan; Teuber, Katharina; Simons, Franz
  • Environmental Earth Sciences, Vol. 74, Issue 11
  • DOI: 10.1007/s12665-015-4726-7

A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow
journal, April 2004


Integral formulation of shallow-water equations with anisotropic porosity for urban flood modeling
journal, November 2008


Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency
journal, June 2012


Unstructured mesh generation and landcover-based resistance for hydrodynamic modeling of urban flooding
journal, December 2008


A model for overland flow and associated processes within the Hydroinformatics Modelling System
journal, March 2014

  • Simons, Franz; Busse, Tobias; Hou, Jingming
  • Journal of Hydroinformatics, Vol. 16, Issue 2
  • DOI: 10.2166/hydro.2013.173

Towards a generalised GPU/CPU shallow-flow modelling tool
journal, December 2013


Experiments of dam-break wave over a triangular bottom sill
journal, December 2007


Dam-break flow through an idealised city
journal, September 2008

  • Soares-Frazão, Sandra; Zech, Yves
  • Journal of Hydraulic Research, Vol. 46, Issue 5
  • DOI: 10.3826/jhr.2008.3164

Two-dimensional shallow-water model with porosity for urban flood modelling
journal, January 2008


A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain
journal, July 2011


Role of microtopography in rainfall-runoff partitioning: An analysis using idealized geometry: MICROTOPOGRAPHY AND RAINFALL-RUNOFF PARTITIONING
journal, July 2010

  • Thompson, Sally E.; Katul, Gabriel G.; Porporato, Amilcare
  • Water Resources Research, Vol. 46, Issue 7
  • DOI: 10.1029/2009WR008835

Restoration of the contact surface in the HLL-Riemann solver
journal, July 1994

  • Toro, E. F.; Spruce, M.; Speares, W.
  • Shock Waves, Vol. 4, Issue 1
  • DOI: 10.1007/BF01414629

Divergence Form for Bed Slope Source Term in Shallow Water Equations
journal, July 2006


Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
journal, July 1979


Integrated mathematical modeling of hydrological and hydrodynamic response to rainfall events in rural lowland catchments
journal, July 2014

  • Viero, D. P.; Peruzzo, P.; Carniello, L.
  • Water Resources Research, Vol. 50, Issue 7
  • DOI: 10.1002/2013WR014293

Urban fluvial flood modelling using a two-dimensional diffusion-wave treatment, part 1: mesh resolution effects
journal, January 2006

  • Yu, D.; Lane, S. N.
  • Hydrological Processes, Vol. 20, Issue 7
  • DOI: 10.1002/hyp.5935

    Works referencing / citing this record:

    Computing flooding of crossroads with obstacles using a 2D numerical model
    journal, September 2017


    Computing flooding of crossroads with obstacles using a 2D numerical model
    text, January 2017