Skip to main content
SpringerLink
Log in

Simulation of dam/levee-break hydrodynamics with a three-dimensional implicit unstructured-mesh finite element model

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

Dam failures usually cause huge economic and life losses , especially in urban areas where there is a high concentration of inhabitants and economic actors. In order to understand the physical mechanisms of the formation and development of dam-break flooding, lots of efforts have been put into different types of modelling techniques. However, most of existing models are 1D (one-dimensional) or 2D models based on the shallow water equations. In this paper, we present a 3D numerical modelling investigation of dam-break flow hydrodynamics in an open L-shape channel. A newly developed 3D unstructured mesh finite element model is used here. An absorption-like term is introduced to the Navier–Stokes equations in order to control the conditioning of the matrix equation in the numerical solution process and thus improve the stability. A wetting and drying algorithm is used here to allow the free surface height to be treated with a high level of implicitness and stability. The 3D model has been validated by comparing the results with the published experimental data. Good agreement has been achieved at six selected locations. This study shows that the 3D unstructured mesh model is capable of capturing the 3D hydraulic aspects and complicated local flows around structures in simulation of dam-break flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Rahman M, Chaudhry MH (1998) Simulation of dam-break flow with grid adaptation. Adv Water Resour 21(1):1–9

    Article  Google Scholar 

  2. Sakkas JG, Strelkoff T (1973) Dam-break flood in a prismatic dry channel. J Hydraul Div 99(12):2195–2216

    Google Scholar 

  3. Chen Cl (1980) Laboratory verification of a dam-break flood model. J Hydraul Div 106(4):535–556

    Google Scholar 

  4. Garcia R, Kahawita R (1986) Numericl solution of the St. Venant equations with the maccormack finite-difference scheme. Int J Numer Meth Fluids 6(5):259–274

    Article  Google Scholar 

  5. Beam R, Warming R (1976) An implicit finite-difference algorithm for hyperbolic systems in coservation-law form. J Comput Phys 22(1):87–110

    Article  Google Scholar 

  6. Roe P (1981) Approximate riemann solvers, parameter vectors, and difference schemes. J Comput Phys 43(2):357–372

    Article  Google Scholar 

  7. Katopodes N (1982) On zero-inertia and kinematic waves. J Hydraul Div 108(11):1380–1387

    Google Scholar 

  8. Zoppou C, Roberts S (1999) Catastrophic collapse of water supply reservoirs in urban areas. J Hydraul Eng 125(7):686–695

    Article  Google Scholar 

  9. Garcia-Navarro P, Fras A, Villanueva I (1999) Dam-break flow simulation: some results for one-dimensional models of real cases. J Hydrol 216(3):227–247

    Article  Google Scholar 

  10. Aureli F, Mignosa P, Tomirotti M (2000) Numerical simulation and experimental verification of dam-break flows with shocks. J Hydraul Res 38(3):197–206

    Article  Google Scholar 

  11. Tseng MH, Chu CR (2000) The simulation of dam-break flows by an improved predictor-corrector TVD scheme. Adv Water Resour 23(6):637–643

    Article  Google Scholar 

  12. Wang JS, Ni HG, He YS (2000) Finite-difference TVD scheme for computation of dam-break problems. J Hydraul Eng 126(4):253–262

    Article  Google Scholar 

  13. Lin GF, Lai JS, Guo WD (2003) Finite-volume component-wise tvd schemes for 2D shallow water equations. Adv Water Resour 26(8):861–873

    Article  Google Scholar 

  14. Liang D, Falconer RA, Lin B (2007) Coupling surface and subsurface flows in a depth averaged flood wave model. J Hydrol 337(1):147–158

    Article  Google Scholar 

  15. Bai Y, Xu D, Lu D (2007) Numerical simulation of two-dimensional dam-break flows in curved channels. J Hydrodyna Ser B 19(6):726–735

    Article  Google Scholar 

  16. Peng SH (2012) 1D and 2D numerical modeling for solving dam-break flow problems using finite volume method. J Appl Math 2012(4):359–373

    Google Scholar 

  17. Brufau P, Garcia-Navarro P (2000) Two-dimensional dam break flow simulation. Int J Numer Meth Fluids 33(1):35–57

    Article  Google Scholar 

  18. Abdolmaleki K, Thiagarajan K, Morris-Thomas M (2004) Simulation of the dam break problem and impact flows using a Navier–Stokes solver. Simulation 13:17

    Google Scholar 

  19. Liang Q, Borthwick A, Stelling G (2004) Simulation of dam-and dyke-break hydrodynamics on dynamically adaptive quadtree grids. Int J Numer Meth Fluids 46(2):127–162

    Article  Google Scholar 

  20. Aliparast M (2009) Two-dimensional finite volume method for dam-break flow simulation. Int J Sedim Res 24(1):99–107

    Article  Google Scholar 

  21. Xia J, Lin B, Falconer RA, Wang G (2010) Modelling dam-break flows over mobile beds using a 2D coupled approach. Adv Water Resour 33(2):171–183

    Article  Google Scholar 

  22. Campisano A, Creaco E, Modica C (2013) Numerical modelling of sediment bed aggradation in open rectangular drainage channels. Urban Water J 10(6):365–376

    Article  Google Scholar 

  23. Kärnä T, Brye B, Gourgue O, Lambrechts J, Comblen R et al (2011) A fully implicit wetting-drying method for dg-fem shallow water models, with an application to the scheldt estuary. Comput Methods Appl Mech Eng 200(5–8):509–524

    Article  Google Scholar 

  24. Kesserwani G, Liang Q (2012) Dynamically adaptive grid based discontinous galerkin shallow water model. Adv Water Resour 37(1):23–39

    Article  Google Scholar 

  25. Begnudelli L, Sanders BF (2007) Simulation of the St. Francis dam-break flood. J Eng Mech 133(11):1200–1212

    Article  Google Scholar 

  26. Larocque LA, Elkholy M, Hanif Chaudhry M, Imran J (2013a) Experiments on urban flooding caused by a levee breach. J Hydraul Eng 139(9):960–973

    Article  Google Scholar 

  27. Yan J, Cao ZX, Liu HH, Chen L (2009) Experimental study of landslide dam-break flood over erodible bed in open channels. J Hydrodyn Ser B 21(1):124–130

    Article  Google Scholar 

  28. Gottardi G, Venutelli M (2004) Central scheme for two-dimensional dam-break flow simulation. Adv Water Resour 27(3):259–268

    Article  Google Scholar 

  29. Biscarini C, Francesco SD, Manciola P (2010) CFD modelling approach for dam break flow studies. Hydrol Earth Syst Sci 14(4):705–718

    Article  Google Scholar 

  30. Yue W, Lin CL, Patel VC (2003) Numerical simulation of unsteady multidimensional free surface motions by level set method. Int J Numer Meth Fluids 42(8):853–884

    Article  Google Scholar 

  31. Zhang Y, Zeng Z, Chen J (2012) The improved space-time conservation element and solution element scheme for two-dimensional dam-break flow simulation. Int J Numer Meth Fluids 68(5):605–624

    Article  Google Scholar 

  32. Zoppou C, Roberts S (2003) Explicit schemes for dam-break simulations. J Hydraul Eng 129(1):11–34

    Article  Google Scholar 

  33. Soares-Frazão S, Zech Y (2008) Dam-break flow through an idealised city. J Hydraul Res 46(5):648–658

    Article  Google Scholar 

  34. Abderrezzak KEK, Paquier A, Mignot E (2009) Modelling flash flood propagation in urban areas using a two-dimensional numerical model. Nat Hazards 50(3):433–460

    Article  Google Scholar 

  35. Gallegos HA, Schubert JE, Sanders BF (2009) Two-dimensional, high-resolution modeling of urban dam-break flooding: a case study of baldwin hills, california. Adv Water Resour 32(8):1323–1335

    Article  Google Scholar 

  36. Wang X, Cao Z, Pender G, Tan G (2010) Modelling of urban flooding due to yangtze river dike break. Proc ICE-Water Manag 164(1):3–14

    Google Scholar 

  37. Wang Y, Liang Q, Kesserwani G, Hall JW (2011) A 2D shallow flow model for practical dam-break simulations. J Hydraul Res 49(3):307–316

    Article  Google Scholar 

  38. Larocque LA, Imran J, Chaudhry MH (2013b) 3d numerical simulation of partial breach dam-break flow using the les and k-turbulence models. J Hydraul Res 51(2):145–157

    Article  Google Scholar 

  39. Zhang T, Feng P, Maksimović v, Bates PD (2016) Application of a three-dimensional unstructured-mesh finite-element flooding model and comparison with two-dimensional approaches. Water Resour Manag 30:1–19

    Article  Google Scholar 

  40. Funke S, Pain C, Kramer S, Piggott M (2011) A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models. Adv Water Resour 34(11):1483–1495

    Article  Google Scholar 

  41. Frazão SS, Zech Y (2002) Dam break in channels with 90 bend. J Hydraul Eng 128(11):956–968

    Article  Google Scholar 

  42. Geuzaine C, Remacle JF (2009) Gmsh: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Meth Eng 79(11):1309–1331

    Article  Google Scholar 

  43. Pain C, Piggott M, Goddard A, Fang F, Gorman G, Marshall D, Eaton M, Power P, De Oliveira C (2005) Three-dimensional unstructured mesh ocean modelling. Ocean Model 10(1):5–33

    Article  Google Scholar 

  44. Kenwright DN, Mallinson GD (1992) A 3-d streamline tracking algorithm using dual stream functions. In: Proceedings of the 3rd conference on Visualization’92, IEEE Computer Society Press, pp 62–68

  45. Frazão SS, Sillen X, Zech Y (1998) Dam-break flow through sharp bends-physical model and 2D Boltzmann model validation. European Commission, Brussels

    Google Scholar 

  46. Rao A, Jain I, Murthy MR, Murty T, Dube S (2009) Impact of cyclonic wind field on interaction of surge-wave computations using finite-element and finite-difference models. Nat Hazards 49(2):225–239

    Article  Google Scholar 

  47. Du J, Fang F, Pain CC, Navon I, Zhu J, Ham DA (2013) Pod reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow. Comput Math Appl 65(3):362–379

    Article  Google Scholar 

  48. Xiao D, Fang F, Buchan AG, Pain CC, Navon IM, Du J, Hu G (2014) Non-linear model reduction for the navier-stokes equations using residual deim method. J Comput Phys 263:1–18

    Article  Google Scholar 

  49. Couplet M, Basdevant C, Sagaut P (2005) Calibrated reduced-order pod-galerkin system for fluid flow modelling. J Comput Phys 207(1):192–220

    Article  Google Scholar 

  50. Liberge E, Hamdouni A (2010) Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder. J Fluids Struct 26(2):292–311

    Article  Google Scholar 

Download references

Acknowledgements

This work was carried out under funding from the National Natural Science Foundation of China (No. 51609165), the Foundation of State Key Laboratory of Hydraulic Engineering Simulation and Safety (Tianjin University, No. HESS-1607), and the China Postdoctoral Science Foundation (No. 2016M591389). The authors would like to thank Prof. Christopher Pain, Prof. Čedo. Maksimović, Prof. Ionel M. Navon, Dr. Alexandros Avdis, Prof. Zhixian Cao for providing advice and help in this research.

Author information

Authors and Affiliations

  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, 300072, China

    Ting Zhang & Ping Feng

  2. Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London, SW7 2BP, UK

    Ting Zhang & Fangxin Fang

Authors
  1. Ting Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fangxin Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ting Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, T., Fang, F. & Feng, P. Simulation of dam/levee-break hydrodynamics with a three-dimensional implicit unstructured-mesh finite element model. Environ Fluid Mech 17, 959–979 (2017). https://doi.org/10.1007/s10652-017-9530-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-017-9530-3

Keywords

Search

Navigation