Flood Modeling in Urban Area Using a Well-Balanced Discontinuous Galerkin Scheme on Unstructured Triangular Grids
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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] Q. Liang, “Flood simulation using a well-balanced shallow flow model,”
J. Hydraul. Eng., vol. 136, no. 9, pp. 669–675, 2010.
[7] G. Kesserwani and Y. Wang, “Discontinuous Galerkin flood model
formulation: Luxury or necessity?” Water Resources Res., vol. 50, no. 8,
pp. 6522–6541, 2014.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] E. F. Toro, Riemann solvers and numerical methods for fluid dynamics:
a practical introduction, third ed. Springer-Verlag, Berlin Heidelberg,
2009.
[15] 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.
[16] 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. [17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[29] 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.
[30] 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.
[31] 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.
[32] 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.
[33] 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.
[34] 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.
[35] 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.
[36] 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.
[37] 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.
[38] 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.
[39] 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.
[40] 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.
[41] 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.
[42] 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.
[43] 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.
[44] 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.
[45] 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.
[46] 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.
[47] 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.
[48] 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.
[49] 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.
[50] 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.
[51] W. Thaker, “Some exact solutions to the nonlinear shallow-water
equations,” J. Fluid Mech., vol. 107, pp. 499–508, 1981.
[52] M. Sun and K. Takayama, “Error localization in solution-adaptive grid
methods,” J. Comput. Phys., vol. 190, no. 1, pp. 346–350, 2003.
[53] 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.
[54] N. Goutal, “The Malpasset dam failure. An overview and test case
definition,” in Proc. of the 4th CADAM meeting, Zaragoza, Spain, 1999.
[55] 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.
[56] 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.
[57] 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.
[58] 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.
[59] 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.
[60] 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.
[61] J. Mulet and F. Alcrudo, “Uncertainty analysis of Tous flood propagation
case study,” in Proc. of the 4rd Impact Project Workshop, Zaragoza,
Spain, 2004.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] Q. Liang, “Flood simulation using a well-balanced shallow flow model,”
J. Hydraul. Eng., vol. 136, no. 9, pp. 669–675, 2010.
[7] G. Kesserwani and Y. Wang, “Discontinuous Galerkin flood model
formulation: Luxury or necessity?” Water Resources Res., vol. 50, no. 8,
pp. 6522–6541, 2014.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] E. F. Toro, Riemann solvers and numerical methods for fluid dynamics:
a practical introduction, third ed. Springer-Verlag, Berlin Heidelberg,
2009.
[15] 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.
[16] 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. [17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[29] 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.
[30] 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.
[31] 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.
[32] 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.
[33] 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.
[34] 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.
[35] 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.
[36] 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.
[37] 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.
[38] 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.
[39] 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.
[40] 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.
[41] 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.
[42] 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.
[43] 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.
[44] 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.
[45] 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.
[46] 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.
[47] 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.
[48] 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.
[49] 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.
[50] 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.
[51] W. Thaker, “Some exact solutions to the nonlinear shallow-water
equations,” J. Fluid Mech., vol. 107, pp. 499–508, 1981.
[52] M. Sun and K. Takayama, “Error localization in solution-adaptive grid
methods,” J. Comput. Phys., vol. 190, no. 1, pp. 346–350, 2003.
[53] 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.
[54] N. Goutal, “The Malpasset dam failure. An overview and test case
definition,” in Proc. of the 4th CADAM meeting, Zaragoza, Spain, 1999.
[55] 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.
[56] 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.
[57] 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.
[58] 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.
[59] 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.
[60] 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.
[61] J. Mulet and F. Alcrudo, “Uncertainty analysis of Tous flood propagation
case study,” in Proc. of the 4rd Impact Project Workshop, Zaragoza,
Spain, 2004.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:78406", author = "Rabih Ghostine and Craig Kapfer and Viswanathan Kannan and Ibrahim Hoteit", title = "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.", keywords = "Flood modeling, dam-break, shallow water equations,
Discontinuous Galerkin scheme, MUSCL scheme.", volume = "13", number = "2", pages = "19-11", }
