Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling

Water Resources Research

Volumn 48, Issue 5, 2012, Pages

  De Almeida, Gustavo A M ^a   Bates, Paul ^a   Freer, Jim E ^a   Souvignet, Maxime ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX TOPOGRAPHIES; COMPUTATIONAL COSTS; COMPUTATIONAL TIME; ENHANCED STABILITY; EXPLICIT EQUATIONS; FLOOD MODELING; FLOOD PROPAGATION; FLOOD RISK ASSESSMENTS; HIGH RESOLUTION; HYDRAULIC FEATURES; HYDRAULIC PROCESS; LOW FRICTION; MODEL PERFORMANCE; NUMERICAL SCHEME; SHALLOW WATER EQUATIONS; SMOOTH SURFACE; STABILITY PROBLEM; TEST CASE; TIME STEP; TWO-DIMENSIONAL HYDRODYNAMICS; UNITED KINGDOM; URBAN AREAS; URBAN DOMAINS; URBANIZED AREA;

FLOOD CONTROL;

EQUATIONS OF MOTION;

COMPLEX TERRAIN; FLOOD CONTROL; FLOODING; HYDRODYNAMICS; NUMERICAL MODEL; RISK ASSESSMENT; SHALLOW-WATER EQUATION; TOPOGRAPHIC EFFECT; TWO-DIMENSIONAL MODELING; URBAN AREA;

ENGLAND; LONDON [ENGLAND]; UNITED KINGDOM;

EID: 84861388543     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011WR011570     Document Type: Article

References (37)

1. Arico, C., M. Sinagra, L. Begnudelli, and T. Tucciarelli (2011), MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes, Adv. Water Resour., 34, 1427-1449, doi:10.1016/ j.advwatres.2011.08.002.
2. Aronica, G., T. Tucciarelli, and C. Nasello (1998), 2D Multilevel model for flood wave propagation in flood-affected areas, J. Water Resour. Plann. Manage., 124, 210-217, doi:10.1061/(ASCE)0733-9496(1998) 124:4(210). (Pubitemid 28466146)
3. Bates, P. D., and A. P. J. De Roo (2000), A simple raster-based model for flood inundation simulation, J. Hydrol., 236, 54-77, doi:10.1016/S0022- 1694(00)00278-X.
4. Bates, P. D., M. S. Horritt, and T. J. Fewtrell (2010), A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling, J. Hydrol., 387, 33-45, doi:10.1016/ j.jhydrol.2010.03. 027.
5. Bermudez, A., C. Rodriguez, and M. A. Vilar (1991), Solving shallow water equations by a mixed implicit finite element method, IMA J. Numer. Anal., 11, 79-97.
6. Bradford, S. F., and B. F. Sanders (2002), Finite-volume model for shallowwater flooding of arbitrary topography, J. Hydraul. Eng., 128, 289-298, doi:10.1061/(ASCE)0733-9429(2002)128:3(289). (Pubitemid 34271564)
7. Bradford, S. F., and B. F. Sanders (2005), Performance of high-resolution, nonlevel bed, shallow-water models, J. Hydraul. Eng., 131, 1073-1081, doi:10.1061/(ASCE)0733-9399(2005)131:10(1073). (Pubitemid 41419839)
8. Brown, J. D., T. Spencer, and I. Moeller (2007), Modeling storm surge flooding of an urban area with particular reference to modeling uncertainties: A case study of Canvey Island, United Kingdom, Water Resour. Res., 43, W06402, doi:10.1029/2005WR004597. (Pubitemid 47124425)
9. Chow, V. T. (1959), Open-Channel Hydraulics, 680 pp., McGraw-Hill, N. Y.
10. Cunge, J. A., F. M. Holly, and A. Verwey (1980), Practical Aspects of Computational River Hydraulics, 420 pp., Pitman, London, U.K.
11. Fewtrell, T. J. (2008), Development of simple methods for two-dimensional hydraulic models of urban flooding, PhD. dissertation submitted to the University of Bristol, Bristol, U.K.
12. Fewtrell, T., P. D. Bates, M. Horritt, and N. Hunter (2008), Evaluating the effect of scale in flood inundation modelling in urban environments, Hydrol. Processes, 22, 5107-5118, doi:10.1002/hyp.
13. Gouldby, B., P. Sayers, O. Tarrant, and D. Kavanagh (2007), Thames Estuary 2100: Performance based asset management, Tech. Rep. IA8/10, HR Wallingford, UK.
14. Gouldby, B., P. Sayers, J. Mulet-Marti, M. A. A. M. Hassan, and D. Benwell (2008), A methodology for regional-scale flood risk assessment, Proceedings of the Institution of Civil Engineers, Water Management, 161, pp. 169-182, doi:10.1680/wama.2008.161.3.169.
15. Guinot, V., and S. Frazão (2006), Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids, Int. J. Numer. Method Fluids, 50, 309-345. (Pubitemid 43085807)
16. Hervouet, J. M. (2000), TELEMAC modelling system: An overview, Hydrol. Processes, 14, 2209-2210, doi:10.1002/1099-1085(200009) 14:13<2209: :AID-HYP23>3.3.CO;2-Y.
17. Hervouet, J. M., and A. Petitjean (1999), Malpasset dam break revisited with two-dimensional computations, J. Hydraul. Res., 37(6), 777-788.
18. Horritt, M. S., and P. D. Bates (2001), Effects of spatial resolution on a raster based model of flood flow, J. Hydrol., 253, 239-249. (Pubitemid 32996495)
19. Hunter, N. M., M. S. Horritt, P. D. Bates, M. D. Wilson, and M. G. F. Werner (2005), An adaptive time step solution for raster-based storage cell modelling of floodplain inundation, Adv. Water Resour., 28, 975- 991, doi:10.1016/j.advwatres.2005.03.007. (Pubitemid 41110302)
20. Hunter, N. M., P. D. Bates, M. S. Horritt, and M. D. Wilson (2006), Improved simulation of flood flows using storage cell models, Proceedings of the Institution of Civil Engineers, Water Manage., 159(1), 9-18. (Pubitemid 43385203)
21. Hunter, N. M., et al. (2008), Benchmarking 2D hydraulic models for urban flooding, WaterManage., 161, 13-30, doi:10.1680/wama.2008.161.1.13. (Pubitemid 351276915)
22. Lax, P., and B. Wendroff (1960), Systems of conservation laws, Commun. Pure Appl. Math., 13(12), 217-237.
23. LeVeque, R. J. (2002), Finite Volume Methods for Hyperbolic Problems, 257 pp., Cambridge Univ. Press, Cambridge, Mass.
24. LeVeque, R. J., and D. L. George (2008), High-resolution finite volume methods for the shallow water equations with bathymetry and dry states, in Advanced Numerical Models for Simulating Tsunami Waves and Runup, Advances in Coastal and Ocean Engineering, vol. 10, edited by P. L. Liu, C. Synolakis, and H. Yeh, pp. 43-73, World Scientific, Singapore, available at http://www.amath.washington.edu/rjl/pubs/catalina04/.
25. Li, S., and C. J. Duffy (2011), Fully coupled approach to modeling shallow water flow, sediment transport, and bed evolution in rivers, Water Resour. Res., 47, W03508, doi:10.1029/2010WR009751.
26. Neal, J., I. Villanueva, N. Wright, T. Willis, T. Fewtrell, and P. Bates (2011a), How much physical complexity is needed to model flood inundation, Hydrol. Processes, doi:10.1002/hyp.8339, in press.
27. Neal, J., G. Schumann, T. Fewtrell, M. Budimir, P. Bates, and D. Mason (2011b), Evaluating a new LISFLOOD-FP formulation with data from the summer 2007 floods in Tewkesbury, UK, J. Flood Risk Manage., 4, 85-95, doi:10.1111/j.1753- 318X.2011.01093.x.
28. Neal, J. C., P. D. Bates, T. J. Fewtrell, N.M. Hunter, M. D.Wilson, and M. S. Horritt (2009), Distributed whole city water level measurements from Carlisle 2005 urban flood event and comparison with hydraulic model simulations, J. Hydrol., 368, 42-55, doi:10.1016/j.jhydrol.2009.01.026.
29. Peraire, J., O. C. Zienkiewicz, and K. Morgan (1986), Shallow water problems: A general explicit formulation, Int. J. Num. Methods Eng., 22, 547-574. (Pubitemid 16538302)
30. Ponce, V. M. (1990), Generalized diffusion wave equation with inertial effects, Water Resour. Res., 26(5), 1099-1101. (Pubitemid 247104)
31. Ponce, V. M., R. M. Li, and D. B. Simons (1978), Applicability of kinematic and diffusion models, J. Hydraul. Eng., 104, 353-360.
32. Sanders, B., J. E. Schubert, and H. A. Gallegos (2008), Integral formulation of shallow-water equations with anisotropic porosity for urban flood modeling, J. Hydrol., 362, 19-38.
33. Toro, E. F. (2001), Shock-capturing methods for free-surface shallow flows, John Wiley, Chichester, U. K.
34. Toro, E. F., and P. Garcia-Navarro (2007), Godunov-type methods for freesurface shallow flows: A review, J. Hydraul. Res., 45(6), 736-751.
35. van Leer, B. (1979), Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys., 32, 101-136.
36. Villanueva, I., and N. G. Wright (2006), Linking Riemann and storage cell models for flood prediction, Proceedings of the Institution of Civil Engineers, Water Management, 159, 27-33. (Pubitemid 43385205)
37. Xia, R. (1994), Impact of coefficients in momentum equation on selection of inertial models, J. Hydraul. Res., 32, 615-621.