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Flood Modeling in Urban Area Using a Well-Balanced Discontinuous Galerkin Scheme on Unstructured Triangular Grids
Abstract:Urban flooding resulting from a sudden release of water due to dam-break or excessive rainfall is a serious threatening environment hazard, which causes loss of human life and large economic losses. Anticipating floods before they occur could minimize human and economic losses through the implementation of appropriate protection, provision, and rescue plans. This work reports on the numerical modelling of flash flood propagation in urban areas after an excessive rainfall event or dam-break. A two-dimensional (2D) depth-averaged shallow water model is used with a refined unstructured grid of triangles for representing the urban area topography. The 2D shallow water equations are solved using a second-order well-balanced discontinuous Galerkin scheme. Theoretical test case and three flood events are described to demonstrate the potential benefits of the scheme: (i) wetting and drying in a parabolic basin (ii) flash flood over a physical model of the urbanized Toce River valley in Italy; (iii) wave propagation on the Reyran river valley in consequence of the Malpasset dam-break in 1959 (France); and (iv) dam-break flood in October 1982 at the town of Sumacarcel (Spain). The capability of the scheme is also verified against alternative models. Computational results compare well with recorded data and show that the scheme is at least as efficient as comparable second-order finite volume schemes, with notable efficiency speedup due to parallelization.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2571881Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 285
 J. Ernst, B. J. Dewals, S. Detrembleur, P. Archambeau, S. Erpicum, and M. Pirotton, “Micro-scale flood risk analysis based on detailed 2d hydraulic modelling and high resolution geographic data,” Nat. Hazards, vol. 55, no. 2, pp. 181–209, 2010.
 L. Song, J. Zhou, J. Guo, Q. Zou, and Y. Liu, “A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain,” Adv. Water Resour., vol. 34, no. 7, pp. 915–932, 2011.
 D. P. Viero, A. D?Alpaos, L. Carniello, and A. Defina, “Mathematical modeling of flooding due to river bank failure,” Adv. Water Resour., vol. 59, pp. 82–94, 2013.
 C. Dawson, C. J. Trahan, E. J. Kubatko, and J. J. Westerink, “A parallel local timestepping runge–kutta discontinuous Galerkin method with applications to coastal ocean modeling,” Comput. Methods Appl. Mech. Engrg., vol. 259, pp. 154–165, 2013.
 K. E. K. Abderrezzak, A. Paquier, and E. Mignot, “Modelling flash flood propagation in urban areas using a two-dimensional numerical model,” Nat. Hazards, vol. 50, no. 3, pp. 433–460, 2009.
 Q. Liang, “Flood simulation using a well-balanced shallow flow model,” J. Hydraul. Eng., vol. 136, no. 9, pp. 669–675, 2010.
 G. Kesserwani and Y. Wang, “Discontinuous Galerkin flood model formulation: Luxury or necessity?” Water Resources Res., vol. 50, no. 8, pp. 6522–6541, 2014.
 D. Sugawara and K. Goto, “Numerical modeling of the 2011 Tohoku-oki tsunami in the offshore and onshore of Sendai Plain, Japan,” Sediment. Geol., vol. 282, pp. 110–123, 2012.
 M. Akbar and S. Aliabadi, “Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling,” Environ. model. softw., vol. 46, pp. 118–128, 2013.
 K. Anastasiou and C. Chan, “Solution of the 2d shallow water equations using the finite volume method on unstructured triangular meshes,” Int. J. Numer. Methods Fluids, vol. 24, no. 11, pp. 1225–1245, 1997.
 T. H. Yoon and S.-K. Kang, “Finite volume model for two-dimensional shallow water flows on unstructured grids,” J. Hydraul. Eng., vol. 130, no. 7, pp. 678–688, 2004.
 A. I. Delis, I. Nikolos, and M. Kazolea, “Performance and comparison of cell-centered and node-centered unstructured finite volume discretizations for shallow water free surface flows,” Arch. Comput. Methods Eng., vol. 18, no. 1, pp. 57–118, 2011.
 J. Murillo and P. Garc´ıa-Navarro, “Improved riemann solvers for complex transport in two-dimensional unsteady shallow flow,” J. Comput. Phys., vol. 230, no. 19, pp. 7202–7239, 2011.
 E. F. Toro, Riemann solvers and numerical methods for fluid dynamics: a practical introduction, third ed. Springer-Verlag, Berlin Heidelberg, 2009.
 B. F. Sanders, “Integration of a shallow water model with a local time step,” J. Hydraul. Res., vol. 46, no. 4, pp. 466–475, 2008.
 D. A. Haleem, G. Kesserwani, and D. Caviedes-Voulli`eme, “Haar wavelet-based adaptive finite volume shallow water solver,” J. Hydroinform., vol. 17, no. 6, pp. 857–873, 2015.
 A. Lacasta, M. Morales-Hern´andez, J. Murillo, and P. Garc´ıa-Navarro, “Gpu implementation of the 2d shallow water equations for the simulation of rainfall/runoff events,” Environ. Earth Sci., vol. 74, no. 11, pp. 7295–7305, 2015.
 P. Brufau, M. V´azquez-Cend´on, and P. Garc´ıa-Navarro, “A numerical model for the flooding and drying of irregular domains,” Int. J. Numer. Methods Fluids, vol. 39, no. 3, pp. 247–275, 2002.
 I. Nikolos and A. Delis, “An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography,” Comput. Methods in Appl. Mech. Engrg., vol. 198, no. 47-48, pp. 3723–3750, 2009.
 Q. Liang and F. Marche, “Numerical resolution of well-balanced shallow water equations with complex source terms,” Adv. water Resour., vol. 32, no. 6, pp. 873–884, 2009.
 J. Hou, Q. Liang, F. Simons, and R. Hinkelmann, “A stable 2d unstructured shallow flow model for simulations of wetting and drying over rough terrains,” Comput. Fluids, vol. 82, pp. 132–147, 2013.
 F. Aureli, A. Maranzoni, P. Mignosa, and C. Ziveri, “A weighted surface-depth gradient method for the numerical integration of the 2d shallow water equations with topography,” Adv. Water Resour., vol. 31, no. 7, pp. 962–974, 2008.
 F. Benkhaldoun, I. Elmahi, and M. Sea¨ıd, “A new finite volume method for flux-gradient and source-term balancing in shallow water equations,” Comput. Methods Appl. Mech. Engrg., vol. 199, no. 49-52, pp. 3324–3335, 2010.
 Y. Wang, Q. Liang, G. Kesserwani, and J. W. Hall, “A 2d shallow flow model for practical dam-break simulations,” J. Hydraul. Res., vol. 49, no. 3, pp. 307–316, 2011.
 J. Hou, Q. Liang, F. Simons, and R. Hinkelmann, “A 2d well-balanced shallow flow model for unstructured grids with novel slope source term treatment,” Adv. Water Resour., vol. 52, pp. 107–131, 2013.
 J. Hou, Q. Liang, H. Zhang, and R. Hinkelmann, “An efficient unstructured muscl scheme for solving the 2d shallow water equations,” Environ. Modell. Softw., vol. 66, pp. 131–152, 2015.
 D. Schwanenberg and M. Harms, “Discontinuous Galerkin finite-element method for transcritical two-dimensional shallow water flows,” J. Hydraul. Eng., vol. 130, no. 5, pp. 412–421, 2004.
 J.-F. Remacle, S. S. Frazao, X. Li, and M. S. Shephard, “An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods,” Int. J. Numer. Methods Fluids, vol. 52, no. 8, pp. 903–923, 2006.
 A. Ern, S. Piperno, and K. Djadel, “A well-balanced runge–kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying,” Int. J. Numer. Methods Fluids, vol. 58, no. 1, pp. 1–25, 2008.
 G. Kesserwani, R. Ghostine, J. Vazquez, A. Ghenaim, and R. Mos´e, “Application of a second-order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms,” Int. J. Numer. Methods Fluids, vol. 56, no. 7, pp. 805–821, 2008.
 S. Bunya, E. J. Kubatko, J. J. Westerink, and C. Dawson, “A wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations,” Comput. Methods Appl. Mech. Engrg., vol. 198, no. 17, pp. 1548–1562, 2009.
 R. Ghostine, G. Kesserwani, J. Vazquez, N. Rivi`ere, A. Ghenaim, and R. Mose, “Simulation of supercritical flow in crossroads: Confrontation of a 2d and 3d numerical approaches to experimental results,” Comput. Fluids, vol. 38, no. 2, pp. 425–432, 2009.
 G. Kesserwani and Q. Liang, “Locally limited and fully conserved rkdg2 shallow water solutions with wetting and drying,” J. Sci. Comput., vol. 50, no. 1, pp. 120–144, 2012.
 Y. Xing and X. Zhang, “Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes,” J. Sci. Comput., vol. 57, no. 1, pp. 19–41, 2013.
 D. Wirasaet, E. Kubatko, C. Michoski, S. Tanaka, J. Westerink, and C. Dawson, “Discontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flow,” Comput. Methods Appl. Mech. engrg., vol. 270, pp. 113–149, 2014.
 N. Wintermeyer, A. R. Winters, G. J. Gassner, and D. A. Kopriva, “An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry,” J. Comput. Phys., vol. 340, pp. 200–242, 2017.
 G. Kesserwani, J. L. Ayog, and D. Bau, “Discontinuous Galerkin formulation for 2d hydrodynamic modelling: Trade-offs between theoretical complexity and practical convenience,” Comput. Methods Appl. Mech. Engrg., vol. 342, pp. 710–741, 2018.
 G. Kesserwani and Q. Liang, “A discontinuous Galerkin algorithm for the two-dimensional shallow water equations,” Comput. Methods Appl. Mech. Engrg., vol. 199, no. 49-52, pp. 3356–3368, 2010.
 D. Caviedes-Voulli`eme and G. Kesserwani, “Benchmarking a multiresolution discontinuous Galerkin shallow water model: Implications for computational hydraulics,” Adv. Water Resour., vol. 86, pp. 14–31, 2015.
 B. Cockburn, S. Hou, and C.-W. Shu, “The Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case,” Math. Comput., vol. 54, no. 190, pp. 545–581, 1990.
 C. Dawson and J. Proft, “Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations,” Comput. Methods Appl. Mech. Engrg., vol. 191, no. 41, pp. 4721–4746, 2002.
 C. Eskilsson, “An hp-adaptive discontinuous Galerkin method for shallow water flows,” Int. J. Numer. Methods Fluids, vol. 67, no. 11, pp. 1605–1623, 2011.
 B. Kim, B. F. Sanders, J. E. Schubert, and J. S. Famiglietti, “Mesh type tradeoffs in 2d hydrodynamic modeling of flooding with a Godunov-based flow solver,” Adv. Water Resour., vol. 68, pp. 42–61, 2014.
 E. Mignot, A. Paquier, and S. Haider, “Modeling floods in a dense urban area using 2D shallow water equations,” J. Hydrol., vol. 327, no. 1, pp. 186–199, 2006.
 J. E. Schubert and B. F. Sanders, “Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency,” Adv. Water Resour., vol. 41, pp. 49–64, 2012.
 M. V. Bilskie and S. C. Hagen, “Topographic accuracy assessment of bare earth lidar-derived unstructured meshes,” Adv. Water Resour., vol. 52, pp. 165–177, 2013.
 M. Hubbard, “Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids,” J. Comput. Phys., vol. 155, no. 1, pp. 54–74, 1999.
 Y. Xing and C.-W. Shu, “A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms,” Commun. Comput. Phys., vol. 1, no. 1, pp. 100–134, 2006.
 L. Begnudelli, B. F. Sanders, and S. F. Bradford, “Adaptive Godunov-based model for flood simulation,” J. Hydraul. Eng., vol. 134, no. 6, pp. 714–725, 2008.
 B. Cockburn and C.-W. Shu, “The Runge–Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems,” J. Comput. Phys., vol. 141, no. 2, pp. 199–224, 1998.
 W. Thaker, “Some exact solutions to the nonlinear shallow-water equations,” J. Fluid Mech., vol. 107, pp. 499–508, 1981.
 M. Sun and K. Takayama, “Error localization in solution-adaptive grid methods,” J. Comput. Phys., vol. 190, no. 1, pp. 346–350, 2003.
 G. Testa, D. Zuccal`a, F. Alcrudo, J. Mulet, and S. Soares-Fraz˜ao, “Flash flood flow experiment in a simplified urban district,” J. Hydraul. Res., vol. 45, no. sup1, pp. 37–44, 2007.
 N. Goutal, “The Malpasset dam failure. An overview and test case definition,” in Proc. of the 4th CADAM meeting, Zaragoza, Spain, 1999.
 A. Valiani, V. Caleffi, and A. Zanni, “Case study: Malpasset dam-break simulation using a two-dimensional finite volume method,” J. Hydraul. Eng., vol. 128, no. 5, pp. 460–472, 2002.
 P. Brufau, P. Garc´ıa-Navarro, and M. V´azquez-Cend´on, “Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography,” Int. J. Numer. Methods Fluids, vol. 45, no. 10, pp. 1047–1082, 2004.
 F. Alcrudo and J. Mulet, “Description of the Tous dam break case study (Spain),” J. Hydraul. Res., vol. 45, no. sup1, pp. 45–57, 2007.
 E. Mignot and A. Paquier, “Impact flood propagation case study: The flooding of Sumac´arcel after Tous dam break, Cemagref modelling,” in Proc. of the 4th Impact Project Workshop, Zaragoza, Spain, 2004.
 J. Mulet and F. Alcrudo, “Impact flood propagation case study: The flooding of Sumac´arcel after Tous dam break, University of Zaragoza modelling,” in Proc. of the 4th Impact Project Workshop, Zaragoza, Spain, 2004.
 S. Soares Frazao and Y. Zech, “The Tous dam break: Description of the simulations performed at UCL,” in Proc. of the 4th Impact Project Workshop, Zaragoza, Spain, 2004.
 J. Mulet and F. Alcrudo, “Uncertainty analysis of Tous flood propagation case study,” in Proc. of the 4rd Impact Project Workshop, Zaragoza, Spain, 2004.