Flood Inundation Modeling with an Adaptive Quadtree Grid Shallow Water Equation Solver
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 11
Abstract
Flood risk studies require hydraulic modeling in order to estimate flow depths and other hydraulic variables in the floodplain for a wide range of input conditions. Currently there is a need to improve the computational efficiency of fully two-dimensional numerical models for large-scale flood simulation. This paper describes an adaptive quadtree grid-based shallow water equation solver and demonstrates its capability for flood inundation modeling. Due to the grid dynamically adapting to dominant flow features such as steep water surface gradients and wet-dry fronts, the approach is both efficient and accurate. The quadtree model is applied to a realistic scenario of flood inundation over an urban area of , resulting from the flood defenses breaching at Thamesmead on the River Thames, United Kingdom. The results of the simulation are in close agreement with alternative predictions obtained using the commercially available software TUFLOW.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The DEM and TUFLOW results for the Thamesmead case study were provided by Professor Gary Pender and Dr. Sylvain Néelz of the United Kingdom Flood Risk Management Research Consortium (EPSRC Grant No. EPSRC-GBGR/S76304/01).
References
Bates, P. D. (2004). “Remote sensing and flood inundation modelling.” Hydrolog. Process., 18, 2593–2597.
Bates, P. D., Anderson, M. G., and Hervouet, J.-M. (1995). “Initial comparison of two 2-dimensional finite element codes for river flood simulation.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 112, 238–248.
Bates, P. D., and de Roo, A. P. J. (2000). “A simple raster-based model for flood inundation simulation.” J. Hydrol., 236, 54–57.
Bradbrook, K. F., Lane, S. N., Waller, S. G., and Bates, P. D. (2004). “Two dimensional diffusion wave modelling of flood inundation using a simplified channel representation.” Int. J. River Basin Management, 3, 1–13.
Brufau, P., García-Navarro, P., and Vázquez-Cendón, M. E. (2004). “Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography.” Int. J. Numer. Methods Fluids, 45, 1047–1082.
Cunge, J. A., Holly, F. M., Jr., and Verwey, A. (1976). Practical aspects of computational river hydraulics, Pitman, London.
Dawson, R. J., and Hall, J. W. (2006). “Adaptive importance sampling for risk analysis of complex infrastructure systems.” Proc. R. Soc. London, Ser. A, 462(2075), 3343–3362.
Dawson, R. J., Hall, J. W., Sayers, P. B., Bates, P. D., and Rosu, C. (2005). “Sampling-based flood risk analysis for fluvial dike systems.” Stochastic Environmental Research and Risk Analysis, 19(6), 388–402.
Galland, J. C., Goutal, N., and Hervouet, J.-M. (1991). “TELEMAC—A new numerical model for solving shall-water equations.” Adv. Water Resour., 14(3), 138–148.
Hall, J. W., Dawson, R. J., Sayers, P. B., Rosu, C., Chatterton, J. B., and Deakin, R. A. (2003). “Methodology for national-scale flood risk assessment.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 156(3), 235–247.
Horritt, M. S., and Bates, P. D. (2001). “Predicting floodplain inundation: raster-based modelling versus the finite element approach.” Hydrolog. Process., 15(5), 825–842.
Horritt, M. S., and Bates, P. D. (2002). “Evaluation of 1D and 2D numerical models for predicting river flood inundation.” J. Hydrol., 268(1–4), 87–99.
HR Wallingford Ltd. (2003). “Flood risks to people. Phase 1.” R&D Technical Rep. No. FD2317, Defra, London.
Krámer, T., and Józsa, J. (2007). “Solution-adaptivity in modelling complex shallow flows.” Comput. Fluids, 36(3), 562–577.
Liang, Q., and Borthwick, A. G. L. (2008). “Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography.” Comput. Fluids.
Liang, Q., Borthwick, A. G. L., and Stelling, G. (2004). “Simulation of dam and dyke-break hydrodynamics on dynamically adaptive quadtree grids.” Int. J. Numer. Methods Fluids, 46, 127–162.
Liang, Q., Zang, J., Borthwick, A. G. L., and Taylor, P. H. (2007). “Shallow flow simulation on dynamically adaptive cut-cell quadtree grids.” Int. J. Numer. Methods Fluids, 53(12), 1777–1799.
Mason, D. C., Cobby, D. M., Horritt, M. S., and Bates, P. D. (2003). “Floodplain friction parameterization in two-dimensional river flood models using vegetation heights derived from airborne scanning laser altimetry.” Hydrolog. Process., 17, 1711–1732.
Mignot, E., Paquier, A., and Haider, S. (2007). “Modeling floods in a dense urban area using 2D shallow water equations.” J. Hydrol., 327(1–2), 186–199.
Néelz, S., et al. (2006). “Using remotely sensed data to support flood modelling.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 159(WM1), 35–43.
Néelz, S., and Pender, G. (2007). “Sub-grid scale parameterisation of 2D hydrodynamic models of inundation in the urban area.” Acta Geophys. Pol., 55(1), 65–72.
Rogers, B. D., Borthwick, A. G. L., and Taylor, P. H. (2003). “Mathematical balancing of flux gradient and source terms prior to using Roe’s approximate Riemann solver.” J. Comput. Phys., 192(2), 422–451.
Rogers, B. D., Fujihara, M., and Borthwick, A. G. L. (2001). “Adaptive Q-tree Godunov-type scheme for shallow water equations.” Int. J. Numer. Methods Fluids, 35, 247–280.
Syme, W. J. (1991). “Dynamically linked two-dimensional/one-dimensional hydrodynamic modelling program for rivers, estuaries & coastal waters.” MEngSc (Research) thesis, Dept. of Civil Engineering, The Univ. of Queensland, Australia.
Tarrant, O., Todd, M., Ramsbottom, D., and Wicks, J. (2005). “2D floodplain modelling in the tidal Thames—Addressing the residual risk.” Journal of the Chartered Institution of Water and Environmental Management, 19(2), 125–134.
U.S. Army Corps of Engineers (USACE). (1996). Risk-based analysis for flood damage reduction studies, manual No. EM 1110-2-1619, Washington, D.C.
van Mierlo, M. C. L. M., Vrouwenvelder, A. C. W. M., Calle, E. O. F., Jonkman, S. N., Bruijn, K. M., and Weerts, A. H. (2007). “Assessment of flood risk accounting for river system behaviour.” J. River Basin Management, 5(2), 93–104.
Wicks, J. M., Syme, B., Hassan, M. A. A. M., Lin, B., and Tarrant, O. (2004). “2D modelling of floodplains—Is it worth the effort?” Proc., 39th Defra Flood and Coastal Management Conf., York, U.K., 10.1.1–10.1.11.
Yu, D., and Lane, S. N. (2006a). “Urban fluvial flood modelling using a two-dimensional diffusion-wave treatment. Part 1: Mesh resolution effects.” Hydrolog. Process., 20, 1541–1565.
Yu, D., and Lane, S. N. (2006b). “Urban fluvial flood modelling using a two-dimensional diffusion-wave treatment. Part 2: Development of a sub-grid-scale treatment.” Hydrolog. Process., 20, 1567–1583.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: May 17, 2007
Accepted: Apr 24, 2008
Published online: Nov 1, 2008
Published in print: Nov 2008
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.