Modeling Rapid Flood Propagation Over Natural Terrains Using a Well-Balanced Scheme
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 7
Abstract
The consequences of rapid and extreme flooding events, such as tsunamis, riverine flooding, and dam breaks show the necessity of developing efficient and accurate tools for studying these flow fields and devising appropriate mitigation plans for threatened sites. Two-dimensional simulations of these flows can provide information about the temporal evolution of water depth and velocities, but the accurate prediction of the arrival time of floods and the extent of inundated areas still poses a significant challenge for numerical models of rapid flows over rough and variable topographies. Careful numerical treatments are required to reproduce the sudden changes in velocities and water depths, evolving under strong nonlinear conditions that often lead to breaking waves or bores. In addition, new controlled experiments of flood propagation in complex geometries are also needed to provide data for testing the models and evaluating their performance in more realistic conditions. This work implements a robust, well-balanced numerical model to solve the nonlinear shallow water equations (NSWEs) in a nonorthogonal boundary fitted curvilinear coordinate system. It is shown that the model is capable of computing flows over highly variable topographies, preserving the positivity of the water depth, and providing accurate predictions for the wetting and drying processes. The model is validated against benchmark cases that consider the use of boundary fitted discretizations of the computational domain. In addition, a laboratory experiment is performed of a rapid flood over a complex topography, measuring the propagation of a dam break wave on a scaled physical model, registering time series of water depth in 19 cross sections along the flow direction. The data from this experiment are used to test the numerical model, and compare the performance of the current model with the numerical results of two other recognized NSWE models, showing that the current model is a reliable tool for efficiently and accurately predicting extreme inundation events and long-wave propagation over complex topographies.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This investigation was supported by ECOS-Conicyt project C07U01. Additional support has been provided by Conicyt Fondef project D11i1119 and Conicyt/Fondap program 15110017. The equipment for the laboratory experiments was supplied by the Instituto Nacional de Hidráulica. The authors also thank the technical support provided by Enrique Rosa and the work of Domenico Sciolla and Eduardo González in the development of the experiments.
References
Ahn, T., and Hosoda, T. (2007). “Depth-averaged model of open-channel flows over an arbitrary 3D surface and its applications to analysis of water surface profile.” J. Hydraul. Eng., 350–360.
ANUGA [Computer software]. Australian National University and Geoscience Australia, Canberra, Australia.
ASCE. (2006). Flood resistant design and construction, Reston, VA.
Audusse, E., Bouchut, F., Bristeau, M., Klein, R., and Benoit, P. (2004). “A fast and stable well-balance scheme with hysdrostatic reconstruction for shallow water flows.” SIAM J. Comput. Sci., 25(6), 2050–2065.
Baghlani, A., Talebbeydokhti, N., and Abedini, M. J. (2008). “A shock-capturing model based on flux-vector splitting method in boundary-fitted curvilinear coordinates.” Appl. Math. Model., 32(3), 249–266.
Bellos, C., Soulis, J., and Sakkas, J. (1992). “Experimental investigation of two-dimensional dam-break induced flows.” J. Hydraul. Res., 30(1), 47–63.
Berger, M., George, D., LeVeque, R., and Mandli, K. (2011). “The Geoclaw software for depth-averaged flows with adaptive refinement.” Adv. Water Resour., 34(9), 1195–1206.
Berger, R., and Stockstill, R. (1995). “Finite-element model for high-velocity channels.” J. Hydraul. Eng., 710–716.
Berthon, C., and Marche, F. (2008). “A positive preserving high order VFRoe scheme for shallow water equations: A class of relaxation schemes.” SIAM J. Sci. Comput., 30(5), 2587–2612.
Bouchut, F. (2004). Nonlinear stability of finite volume methods for hyperbolic conservation laws, Basel, Switzerland.
Brufau, P., and García-Navarro, P. (2003). “Unsteady free surface flow simulation over complex topography with multidimensional upwind technique.” J. Comput. Phys., 186(2), 503–526.
Brufau, P., Vásquez-Cendón, M., and García-Navarro, P. (2002). “A numerical model for the flooding and drying of irregular domain.” Int. J. Numer. Method. Fluids, 39(3), 247–275.
Burguete, J., García-Navarro, P., and Murillo, J. (2008). “Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: Application to unsteady irrigation and river flow.” Int. J. Numer. Method. Fluids, 58(4), 403–425.
Cao, Z., Pender, G., Wallis, S., and Carling, P. (2004). “Computational dam-break hydraulics over erodible sediment bed.” J. Hydraul. Eng., 689–703.
Cenderelli, D., and Wohl, E. (2001). “Peak discharge estimates of glacial-lake outburst floods and normal climatic floods in the Mount Everest region, Nepal.” Geomorphology, 40(1–2), 57–90.
Cienfuegos, R., Barthelemy, E., and Bonneton, P. (2007). “A fourth order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations—Part II: Boundary conditions and validation.” Int. J. Numer. Method. Fluids, 53(9), 1423–1455.
Clawpack Version 4.6.3 [Computer software]. University of Washington, Clawpack Development Team, Seattle.
Cunge, J., Holly, F., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman Publishing, London.
Dussaillant, A., Benito, G., Buytaert, W., Carling, P., Meier, C., and Espinoza, F. (2009). “Repeated glacial-lake outburst floods in Patagonia: An increasing hazard?.” Nat. Hazards, 54(2), 469–481.
FEMA. (2011). Coastal construction manual: Principles and practices of planning, siting, designing, constructing, and maintaining residential buildings in coastal areas, 4th Ed., FEMA, Washington, DC.
Fritz, H., et al. (2011). “Field survey of the 27 February 2010 Chile tsunami.” Pure Appl. Geophys., 168(11), 1989–2010.
Gallardo, C., Parés, M., and Castro, M. (2007). “On a well-balanced higher-order finite volume scheme for shallow water equations with topography and dry areas.” J. Comput. Phys, 227(1), 574–601.
Gallouet, T., Herard, J.-M., and Seguin, N. (2003). “Some approximate Godunov scheme to compute shallow-water equations with topography.” Comput. Fluids, 32(4), 479–513.
Greenberg, J., and Leroux, A. (1996). “A well-balanced scheme for the numerical processing of source terms in hyperbolic equations.” SIAM J. Numer. Anal., 33(1), 1–16.
Hibberd, S., and Peregrine, D. (1979). “Surf and run-up on a beach: A uniform bore.” J. Fluid Mech., 95(2), 323–345.
Kawahara, M., and Umetsu, T. (1986). “Finite element method for moving boundary problems in river flow.” Int. J. Numer. Methods Fluids, 6(6), 365–386.
Lackey, T., and Sotiropoulos, F. (2005). “Role of artificial dissipation scaling and multigrid acceleration in numerical solution of the depth-averaged free-surface flow equations.” J. Hydraul. Eng., 476–487.
Lay, L., Ammon, C., Kanamori, H., Koper, K., Sufri, O., and Hutko, A. (2010). “Teleseismic inversion for rupture process of the 27 February 2010 Chile (mw 8.8) earthquake.” Geophys. Res. Lett., 37(13), L13301.
LeVeque, R. (1998). “Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm.” J. Comput. Phys., 146(1), 346–365.
LeVeque, R. (2002). Finite volume methods for hyperbolic problems, Cambridge University Press, Cambridge, U.K.
Liang, D., Lin, B., and Falconer, R. (2007). “A boundary-fitted numerical model for flood routing with shock-capturing capability.” J. Hydrol., 332(3–4), 477–486.
Liang, Q., and Marche, F. (2009). “Numerical resolution of well-balanced shallow water equations with complex source terms.” Adv. Water Resour., 32(6), 873–884.
Loose, B., Niño, Y., and Escauriaza, C. (2005). “Finite volume modeling of variable density shallow-water flow equations for a well-mixed estuary: Application to the Rio Maipo estuary in central Chile.” J. Hydraul. Res., 43(4), 339–350.
Marche, F., Bonneton, P., Fabrie, P., and Seguin, N. (2007). “Evaluation of well-balance bore-capturing schemes for 2D wetting and drying processes.” Int. J. Numer. Methods Fluids, 53(5), 867–894.
Masella, J.-M, Faille, I., and Gallouët, T. (1999). “On an approximate godunov scheme.” Int. J. Comput. Fluid Dyn., 12(2), 133–149.
Molls, T., and Chaudry, D. (1995). “Depth-averaged open-channel flow model.” J. Hydraul. Eng., 453–465.
Molls, T., and Zhao, G. (2000). “Depth-averaged simulation of supercritical flow in channel with wavy sidewall.” J. Hydraul. Eng., 437–444.
Mungkasi, S., and Roberts, S. G. (2013). “Validation of ANUGA hydraulic model using exact solutions to shallow water wave problems.” J. Phys., 423, 24–25.
Nikolos, I., and Delis, A. (2009). “An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography.” Comput. Method. Appl. Mech. Eng., 198(47–48), 3723–3750.
Saint-Venant, Barré de (1971). “Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit.” C.R. (Comptes Rendus des Séances de l'Académie des Sciences. Paris.), 73, 147–154, 237–240.
Sanders, B. (2002). “Non-reflecting boundary flux function for finite volume shallow water models.” Adv. Water Resour., 25(2), 195–202.
Stoker, J. (1992). Water waves, the mathematical theory with applications, Wiley, New York.
Toro, E. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, New York.
Tucciarelli, T., and Termini, D. (2000). “Finite-element modeling of floodplain flow.” J. Hydraul. Eng., 416–424.
Valiani, A., Caleffi, V., and Zanni, A. (2002). “Case study: Malpasset dam-break simulation using a two-dimensional finite volume method.” J. Hydraul. Eng., 460–472.
Van Leer, B. (1979). “Toward the ultimate conservative difference scheme V. A second order sequel to Godunov’s method.” J. Comput. Phys., 32(1), 101–136.
Vasquez, J., Steffler, P., and Millar, R. (2008). “Modeling bed changes in meandering rivers using triangular finite elements.” J. Hydraul. Eng., 1348–1352.
Yamazaki, Y., and Cheung, K. (2011). “Shelf resonance and impact of near field tsunami generated by the 2010 Chile earthquake.” Geophys. Res. Lett., 38(12), 12605–12612.
Yeh, H. (1991). “Tsunami bore runup.” Nat. Hazards, 4(2–3), 209–220.
Yeh, H. (2006). “Maximum fluid forces in the tsunami runup zone.” J. Waterway, Port, Coastal, Ocean Eng., 496–500.
Zhou, J., Causon, D., Mingham, C., and Ingram, D. (2004). “Numerical prediction of dam-break flows in general geometries with complex topography.” J. Hydraul. Eng., 332–340.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 7 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Apr 7, 2013
Accepted: Feb 4, 2014
Published online: Mar 17, 2014
Published in print: Jul 1, 2014
Discussion open until: Aug 17, 2014
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.