Abstract
A coupled 1D–2D hydrodynamic model linking the channel and flood detention basin for flood simulation with complex topography and irregular boundary was presented in this paper. The 1D Saint-Venant equations were used for governing flows in channel, and the four-point implicit Preissmann scheme was used for discretization. To simulate floods in flood detention basin, the 2D shallow equations were adopted as governing equations, and a well-balanced, unstructured finite-volume method was proposed for the numerical resolution. The 2D model is based on a new formulation of the classical shallow water equations in hyperbolic conservation form. The numerical fluxes are computed by HLLC algorithm, and the MUSCL–Hancock predictor–corrector scheme is used to achieve high-accuracy and high-resolution results. A simple and efficient method was proposed to reflect the coupled hydraulic connection between the channel and the flood detention basin. The novelties of the proposed model include (1) a robust method for wetting/drying treatment and (2) an efficient way to link the 1D and 2D models. The 1D, 2D, and coupled models are all tested through some benchmark cases, and numerical results validated the accuracy of the models. Furthermore, the coupled 1D–2D model was used for a real flood simulation in Jiakouwa flood detention basin, China. The flood-risk information including flood arrival time and maximal water depth was mapped using GIS. Those flood-risk maps can be used as an important decision-making basis of flood control and rescue for the flood control departments at all levels.
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References
Aureli F, Maranzoni A, Mignosa P, Ziveri C (2008) A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography. Adv Water Resour 31(7):962–974
Begnudelli L, Sanders BF (2006) Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying. ASCE J Hydraul Eng 132(4):371–384
Blade E, Gomez-Valentin M, Dolz J et al (2012) Integration of 1D and 2D finite volume schemes for computations of water flow in natural channels. Adv Water Resour 42:17–29
Chau KW, Lee JH (1991) Mathematical modelling of Shing Mun River network. Adv Water Resour 14(3):106–112
Islam A, Raghuwanshi NS, Singh R, Sen DJ (2005) Comparison of gradually varied flow computation algorithms for open-channel network. ASCE J Irrig Drain Eng 131(5):457–465
Lai X, Wang D (2002) 1-D and 2-D coupling numerical model of unsteady flow. Hydro Sci Eng 2:48–51 (in Chinese)
Liang Q, Borthwick AGL (2009) Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Comput Fluids 38(2):221–234
Liang D, Falconer RA, Lin B (2007) Linking one-and two-dimensional models for free surface flows. Proc ICE Water Manag 160(3):145–151
Liu Y, Zhou J, Song L, Zou Q, Liao L, Wang Y (2013) Numerical modelling of free-surface shallow flows over irregular topography with complex geometry. Appl Math Model 37(23):9482–9498
Sanders BF, Schubert JE, Detwiler RL (2010) ParBreZo: a parallel, unstructured grid, Godunov-type, shallow-water code for high-resolution flood inundation modeling at the regional scale. Adv Water Resour 33(12):1456–1467
Sen DJ, Garg NK (2002) Efficient algorithm for gradually varied flows in channel networks. ASCE J Irrig Drain Eng 128(6):351–357
Song L, Zhou J, Guo J, Zou Q, Liu Y (2011a) A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain. Adv Water Resour 34(7):915–932
Song L, Zhou J, Li Q, Yang X, Zhang Y (2011b) An unstructured finite volume model for dam- break floods with wet/dry fronts over complex topography. Int J Numer Meth Fluids 67(8):960–980
Xu Z, Yin H (2003) Development of two-dimensional hydrodynamic and water quality model for Huangpu River. J Hydrodyn Ser B 15(2):1–11
Zhu Y, Yan Y, Li R (2003) A coupled hydrodynamic numerical model for bay-river network. Adv Water Sci 14(2):131–135 (in Chinese)
Zhu D, Chen Y, Wang Z, Liu Z (2011) Simple, robust, and efficient algorithm for gradually varied subcritical flow simulation in general channel networks. ASCE J Hydraul Eng 137(7):766–774
Acknowledgments
This work was supported by the National Basic Research Program of China (Project No. 2011CB403305) and the National Non-Profit Research Program of China (Project No. 201301063-03).
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Liu, Q., Qin, Y., Zhang, Y. et al. A coupled 1D–2D hydrodynamic model for flood simulation in flood detention basin. Nat Hazards 75, 1303–1325 (2015). https://doi.org/10.1007/s11069-014-1373-3
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DOI: https://doi.org/10.1007/s11069-014-1373-3