Coupled 1D–Quasi-2D Flood Inundation Model with Unstructured Grids
Publication: Journal of Hydraulic Engineering
Volume 136, Issue 8
Abstract
A simplified numerical model for simulation of floodplain inundation resulting from naturally occurring floods in rivers is presented. Flow through the river is computed by solving the de Saint Venant equations with a one-dimensional (1D) finite volume approach. Spread of excess flood water spilling overbank from the river onto the floodplains is computed using a storage cell model discretized into an unstructured triangular grid. Flow exchange between the one-dimensional river cells and the adjacent floodplain cells or that between adjoining floodplain cells is represented by diffusive-wave approximated equation. A common problem related to the stability of such coupled models is discussed and a solution by way of linearization offered. The accuracy of the computed flow depths by the proposed model is estimated with respect to those predicted by a two-dimensional (2D) finite volume model on hypothetical river-floodplain domains. Finally, the predicted extent of inundation for a flood event on a stretch of River Severn, United Kingdom, by the model is compared to those of two proven two-dimensional flow simulation models and with observed imagery of the flood extents.
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Acknowledgments
The second writer thankfully acknowledges the support of the Commonwealth Scholarship Commission in the United Kingdom for providing a fellowship that enabled him to spend some time at the University of Bristol, U.K., where part of this work was carried out.
References
Bates, P. D., and Anderson, M. G. (1993). “A two-dimensional finite-element model for river flow inundation.” Proc. R. Soc. London, Ser. A, 440, 481–491.
Bates, P. D., and De Roo, A. P. J. (2000). “A simple raster based model for flood inundation simulation.” J. Hydrol., 236, 54–77.
Bates, P. D., Wilson, M. D., Horritt, M. S., Mason, D. C., Holden, N., and Currie, A. (2006). “Reach scale floodplain inundation dynamics observed using airborne synthetic aperture radar imagery: Data analysis and modelling.” J. Hydrol., 328, 306–318.
Bechteler, W., Hartman, S., and Otto, A. (1994). “Coupling of 2D and 1D models and integration into geographic information systems GIS.” River flood hydraulics, W. White and J. Watts, eds., Wiley, New York, 155–165.
Beffa, C., and Connell, R. J. (2001). “Two-dimensional flood plain flow. I: Model description.” J. Hydrol. Eng., 6(5), 397–405.
Begnudelli, L., Sanders, B. F., and Bradford, S. F. (2008). “Adaptive Godunov-based model for flood simulation.” J. Hydraul. Eng., 134(6), 714–725.
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. Riv. Basin. Manag, 2(3), 211–223.
Chang, T. -J., Hsu, M. -H., and Huang, C. -J. (2000). “A GIS distributed watershed model for simulating flooding and inundation.” J. Am. Water Resour. Assoc., 36, 975–988.
Cobby, D. M., Mason, D. C., and Davenport, I. J. (2001). “Image processing of airborne scanning laser altimetry for improved river flood modelling.” ISPRS J. Photogramm. Remote Sens., 56, 121–138.
Crossley, A. J. (1999). “Accurate and efficient numerical solutions for the Saint Venant equations of open channel flow.” Ph.D. thesis, Univ. of Nottingham, Nottingham, U.K.
Cunge, J. A. (1975). “Section 17: Two-dimensional modelling of flood plains.” Unsteady flow in open channels, K. Mahmood and V. Yevjevich, eds., Vol. II, Water Resources Publication, Colo., 17.705–17.762.
Cunge, J. A., Holly, F. M., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman Publishing Limited, London.
Delis, A. I., Skeels, C. P., and Ryrie, S. C. (2000). “Implicit-high resolution methods for modelling one-dimensional open channel flow.” J. Hydraul. Res., 38, 369–382.
Dhondia, J. F., and Stelling, G. S. (2002). “Application of one dimensional-two-dimensional integrated hydraulic model for flood simulation and damage assessment.” Proc., 5th Int. Conf. on Hydroinformatics 2002, R. Falconer, B. Bin, E. Harris, and C. Wilson, eds., IWA Publishing, London, U.K., 265–276.
Dutta, D., Herath, S., and Musiake, K. (2000). “Flood inundation simulation in a river basin using a physically distributed hydrological model.” Hydrolog. Process., 14, 497–519.
Ervine, D. A., and MacCleod, A. B. (1999). “Modelling a river channel with distant floodbanks.” Proc., Institution of Civil Engineers, Water Maritime and Energy, Vol. 136, Telford, London, U.K., 21–33.
Fleming, G., Frost, L., Huntington, S., Knight, D., Law, F., and Rickard, C. (2001). “Learning to live with rivers: Final report of the Institution of Civil Engineers’ Presidential Commission to review the technical aspects of flood risk management in England and Wales.” Institution of Civil Engineers, London, 87.
García-Navarro, P., and Savirón, J. (1992). “McCormack’s method for the numerical simulation of one-dimensional discontinuous unsteady open channel flow.” J. Hydraul. Res., 30, 95–105.
Han, K. -Y., Lee, J. -T., and Park, J. -H. (1998). “Flood inundation analysis resulting from levee break.” J. Hydraul. Res., 36, 747–759.
Hervouet, J., and Haren, L. V. (1996). “Recent advances in numerical methods for fluid flows.” Floodplain processes, Wiley, New York, 182–214.
Hervouet, J. -M., and Janin, J. -M. (1994). “Finite element algorithms for modelling flood propagation.” Modelling flood propagation over initially dry areas, P. Molinaro and L. Natale, eds., ASCE, Reston, Va., 101–113.
Horritt, M. S. (2004). “Development and testing of a simple 2-D finite volume model for sub-critical shallow flow.” Int. J. Numer. Methods Fluids, 44, 1231–1255.
Horritt, M. S., and Bates, P. D. (2001). “Predicting floodplain inundation: raster-based modelling versus the finite element approach.” Hydrolog. Process., 15, 825–842.
Horritt, M. S., Di Baldassarre G., Bates, P. D., and Barth, A. (2007). “Comparing the performance of a 2-D finite volume model of floodplain inundation using airborne SAR imagery.” Hydrolog. Process., 21, 2745–2759.
Hubbard, M. E. (1999). “Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids.” J. Comput. Phys., 155, 54–74.
Hunter, N. M., Horritt, M. S., Bates, P. D., Wilson, M. D., and Werner, M. G. F. (2005). “An adaptive time step solution for raster-based storage cell modelling of floodplain inundation.” Adv. Water Resour., 28, 975–991.
Kuiry, S. N. (2007) “Development of finite volume shallow water flow models and application to floodplain inundation.” Ph.D. thesis, Indian Institute of Technology, Kharagpur, India.
Kuiry, S. N., Pramanik, K., and Sen, D. (2008). “Finite volume model for shallow water equations with improved treatment of source terms.” J. Hydraul. Eng., 134(2), 231–242.
Laura, R. A., and Wang, J. D. (1984). “Two-dimensional flood routing on steep slope.” J. Hydraul. Eng., 110(8), 1121–1135.
Li, B., Phillips, M., and Fleming, C. A. (2006). “Application of 3D hydrodynamic model to flood risk assessment.” Proc. Inst. Civil Engrs. Water Management, 159(WM1), 63–75.
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, 1777–1799.
Lin, B., Wicks, J. M., and Falconer, R. A. (2006). “Integrating 1D and 2D hydrodynamic models for flood simulation.” Proc. Inst. Civil Engrs. Water Management, 159(WM1), 19–25.
Marsh, T. J., and Dale, M. (2002). “The UK floods of 2000–2001: A hydrometeorological appraisal.” J. Chart. Inst. Water Environ. Manag., 16(3), 180–188.
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.
Roe, P. L. (1981). “Approximate Riemann solvers, parameter vectors and difference schemes.” J. Comput. Phys., 43, 357–372.
Samuels, P. G. (1990). “Cross section location in one-dimensional models.” Int. Conf. on River Flood Hydraulics, W. R. White, ed., Wiley, Chichester, 339–350.
Sanders, B. F., Jaffe, D. A., and Chu, A. K. (2003). “Discretization of integral equations describing flow in nonprismatic channels with uneven beds.” J. Hydraul. Eng., 129(3), 235–244.
Schubert, J. E., Sanders, B. F., Smith, M. J., and Wright, N. G. (2008). “Unstructured mesh generation and landcover-based resistance for hydrodynamic modelling of urban flooding.” Adv. Water Resour., 31, 1603–1621.
Sen, D. (2002). “An algorithm for coupling 1D river flow and quasi 2D flood inundation flow.” Proc., 5th Int. Conf. on Hydroinformatics 2002, R. Falconer, B. Bin, E. Harris, and C. Wilson, eds., IWA Publishing, London, U.K., 102–108.
Sen, D. J., and Garg, N. K. (2002). “Efficient algorithm for gradually varied flows in channel networks.” J. Irrig. Drain. Eng., 128(6), 351–357.
Shewchuk, J. R. (1996). “Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator.” Lect. Notes Comput. Sci., 1148, 203–222.
Stelling, G. S., and Verwey, A. (2005). “Numerical flood simulation.” Encyclopaedia of hydrological sciences, Wiley, U.K.
Thomas, T. G., and Williams, J. J. R. (1994). “Large eddy simulation of turbulent flow in an asymmetric compound channel.” J. Hydraul. Res., 33(1), 27–41.
Tuitoek, D. K., and Hicks, F. E. (2001). “Modelling of unsteady flow in compound channels.” J. Civ. Eng., 6, 45–54.
Villanueva, I., and Wright, N. G. (2006). “Linking Riemann and storage cell models for flood prediction.” Proc. Inst. Civil Engrs. Water Management, 159(WM1), 27–33.
Younis, B. A. (1996). “Progress in turbulence modelling for open channel flows.” Floodplain processes, M. G. Anderson, D. E. Walling, and P. D. Bates, eds., Wiley, Chichester, 299–332.
Zanobetti, D., Lorgere, H. G., Preissmann, A., and Cunge, J. A. (1970). “Mekong delta mathematical model program construction.” J. Wtrwy. and Harb. Div., 97, 181–199.
Zhou, J. G., Causon, D. M., Mingham, C. G., and Ingram, D. M. (2001). “The surface gradient method for the treatment of source terms in the shallow-water equations.” J. Comput. Phys., 168, 1–25.
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Published In
Journal of Hydraulic Engineering
Volume 136 • Issue 8 • August 2010
Pages: 493 - 506
Copyright
© 2010 ASCE.
History
Received: Oct 21, 2008
Accepted: Feb 17, 2010
Published online: Feb 20, 2010
Published in print: Aug 2010
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