Integrated hydrodynamic model for simulation of river-lake-sluice interactions.

*(English)*Zbl 07203939Summary: In this paper, an integrated model for simulating the hydrodynamic process of river-lake-sluice (RLS) systems is presented. It includes a novel one-dimensional (1D) and two-dimensional (2D) coupling method called the coupling-zone iteration-correction (CZIC) method, and an improved numerical algorithm for the sluice problem. The 1D river-network model and the 2D lake model are coupled by establishing a coupling region, and iterative correction is carried out to ensure the accurate transfer of hydraulic parameters. The convergence conditions of the CZIC method are discussed theoretically, and the proper spatial step of the coupling zone is adopted according to different inflow conditions to ensure stable computation. In order to deal with the transition of flow regimes during the gate operation, a method for calculating the discharge capacity is presented. In addition, a general difference coefficient of the river reach is deduced for hydrodynamic calculation with sluices included. Simulations on open channels demonstrate that (1) simulated values of the CZIC method are consistent with the results of the full 2D model; (2) the sluice solving algorithm can stably handle the flow transition between the orifice flow and weir flow. Furthermore, the developed integrated model is applied to the middle and lower reaches of the Huaihe River, including the Hongze Lake and fifteen sluices. Numerical simulation results reproduced the hydrodynamic process during the flood season of 2007 accurately and efficiently. The errors of the present model are also compared with that of the MIKE model, and the results show that the proposed methods perform better than MIKE, especially in rising and flood periods. Therefore, it seems likely that the developed integrated model will work well in hydrodynamic modelling of large-scale complex RLS systems.

##### Keywords:

river-lake-sluice system; 1D-2D coupling; iteration-correction method; convergence condition; sluice simulation; Huaihe River Basin
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\textit{C. Zhang} et al., Appl. Math. Modelling 83, 90--106 (2020; Zbl 07203939)

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##### References:

[1] | Plate, E. J., Flood risk and flood management, J. Hydrol., 267, 2-11 (2005) |

[2] | Cozzolino, L.; Cimorelli, L.; Covelli, C.; Della Morte, R.; Pianese, D., The analytic solution of the Shallow-Water Equations with partially open sluice-gates: the dam-break problem, Adv. Water Resour., 80, 90-102 (2015) |

[3] | Demuren, A. O., A numerical model for flow in meandering channels with natural bed topography, Water Resour. Res., 29, 1269-1277 (1993) |

[4] | Shams, M.; Ahmadi, G.; Smith, D. H., Computational modeling of flow and sediment transport and deposition in meandering rivers, Adv. Water Resour., 25, 689-699 (2002) |

[5] | Zhu, H.; Wang, L.; Avital, E. J.; Tang, H.; Williams, J. J.R., Numerical simulation of interaction between internal solitary waves and submerged ridges, Appl. Ocean Res., 58, 118-134 (2016) |

[6] | Liu, Q.; Qin, Y.; Zhang, Y.; Li, Z., Coupled 1D-2D hydrodynamic model for flood simulation in flood detention basin, Nat. Hazards, 75, 1303-1325 (2012) |

[7] | Hu, Z.; Wang, L.; Tang, H.; Qi, X., Prediction of the future flood severity in plain river network region based on numerical model: a case study, J. Hrdrodyn., 04, 62-71 (2017) |

[8] | Paz, A. R.; Bravo, J. M.; Allasia, D.; Collischonn, W.; Tucci, C. E.M., Large-scale hydrodynamic modeling of a complex river network and floodplains, ASCE J. Hydrol. Eng., 15, 152-165 (2010) |

[9] | Liu, Y.; Zhou, J.; Song, L.; Zou, Q.; Liao, L.; Wang, Y., Numerical modelling of free-surface shallow flows over irregular topography with complex geometry, Appl. Math. Model., 37, 9482-9498 (2013) · Zbl 1427.76163 |

[10] | Zhao, D.; Shen, H. W.; Tabios, G. Q.; Lai, J. S.; Tan, W. Y., Finite-Volume two-dimensional unsteady-flow model for river basins, ASCE J. Hydraul. Eng., 120, 863-883 (1994) |

[11] | Chen, W.; Liu, W.; Wu, C., Coupling of a one-dimensional river routing model and a three-dimensional ocean model to predict overbank flows in a complex river-ocean system, Appl. Math. Model., 37, 6163-6176 (2013) |

[12] | Nguyen, V. T., 3D numerical simulation of free surface flows over hydraulic structures in natural channels and rivers, Appl. Math. Model., 39, 6285-6306 (2015) · Zbl 1443.76057 |

[13] | Fernández-Nieto, E. D.; Marin, J.; Monnier, J., Coupling superposed 1D and 2D shallow-water models: source terms in finite volume schemes, Comput. Fluids, 39, 1070-1082 (2010) · Zbl 1242.76162 |

[14] | Han, D.; Fang, H.; Bai, J.; He, G., A coupled 1D and 2D channel network mathematical model used for flow calculations in the middle reaches of the Yangtze river, J. Hrdrodyn., 23, 521-526 (2011) |

[15] | Timbadiya, P. V.; Patel, P. L.; Porey, P. D., A 1D-2D coupled hydrodynamic model for river flood prediction in a coastal urban floodplain, ASCE J. Hydrol. Eng., 20, 17-33 (2015) |

[16] | Zhang, X.; Wang, G.; Jin, S., 1-D and 2-D zonal coupling algorithm for flow and sediment transport, Adv. Water Sci., 15, 151-155 (2004), [in Chinese] |

[17] | Ghostine, R.; Hoteit, I.; Vazquez, J.; Terfous, A.; Ghenaim, A.; Mose, R., Comparison between a coupled 1D-2D model and a fully 2D model for supercritical flow simulation in crossroads, J. Hydraul. Res., 53, 274-281 (2015) |

[18] | Jaafar, H. H.; Merkley, G. P., High-resolution method for modeling hydraulic regime changes at canal gate structures, ASCE J. Irrig. Drainage Eng., 136, 795-808 (2010) |

[19] | Feng, P.; Rui, X., Method of flood routing for multibranch rivers, ASCE J. Hydraul. Eng., 125, 271-276 (1999) |

[20] | Chen, Y.; Wang, Z.; Liu, Z.; Zhu, D., 1D-2D coupled numerical model for shallow-water flows, ASCE J. Hydraul. Eng., 138, 122-132 (2012) |

[21] | Bladé, E.; Gómez-Valentín, M.; Dolz, J.; Aragón-Hernández, J. L.; Corestein, G.; Sánchez-Juny, M., Integration of 1D and 2D finite volume schemes for computations of water flow in natural channels, Adv. Water Resour., 42, 17-29 (2012) |

[22] | Lai, X.; Jiang, J.; Liang, Q.; Huang, Q., Large-scale hydrodynamic modeling of the middle Yangtze River Basin with complex river-lake interactions, J. Hydrol., 492, 228-243 (2013) |

[23] | Morales-Hernández, M.; Petaccia, G.; Brufau, P.; García-Navarro, P., Conservative 1D-2D coupled numerical strategies applied to river flooding: the Tiber (Rome), Appl. Math. Model., 40, 2087-2105 (2016) · Zbl 1452.76126 |

[24] | Barthélémy, S.; Ricci, S.; Morel, T.; Goutal, N.; Le Pape, E.; Zaoui, F., On operational flood forecasting system involving 1D/2D coupled hydraulic model and data assimilation, J. Hydrol., 516, 623-634 (2018) |

[25] | Cunge, J. A.; Holly, F. M.; Verwey, A., Practical Aspects of Computational River Hydraulics (1980), Pitman Publishing Ltd.: Pitman Publishing Ltd. London |

[26] | Meire, D.; Doncker, L. D.; Declercq, F.; Buis, K.; Troch, P.; Verhoeven, R., Modelling river-floodplain interaction during flood propagation, Nat. Hazards, 55, 111-121 (2010) |

[27] | Young, D. M., Iterative Solution of Large Linear Systems (1971), Academic Press: Academic Press New York · Zbl 0231.65034 |

[28] | Roe, P. L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 135, 250-258 (1997) · Zbl 0890.65094 |

[29] | Bermudez, A.; Vazquez, M. E., Upwind methods for hyperbolic conservation laws with source terms, Comput. Fluids, 23, 1049-1071 (1994) · Zbl 0816.76052 |

[30] | Wang, Z.; Geng, Y.; Jin, S., An unstructured finite-volume for nonlinear two-dimensional shallow water equation, J. Hrdrodyn., 17, 306-312 (2005) · Zbl 1207.76097 |

[31] | Sleigh, P. A.; Gaskell, P. H.; Berzins, M.; Wright, N. G., An unstructured finite-volume algorithm for predicting flow in rivers and estuaries, Comput. Fluids, 27, 479-508 (1998) · Zbl 0964.76051 |

[32] | Song, L.; Zhou, J.; Guo, J.; Zou, Q.; Liu, Y., A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain, Adv. Water Resour., 34, 915-932 (2011) |

[33] | Hasselblatt, B.; Katok, A., A First Course in Dynamics (2003), Cambridge University Press: Cambridge University Press New York · Zbl 1027.37001 |

[34] | Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046 |

[35] | Zhang, X.; Fan, W.; Zhang, H., Discharge capacity of low head sluice, J. Hydraul. Eng., 36, 1246-1251 (2005), [in Chinese] |

[36] | Wang, C.; Li, G., Practical River Network Flow Calculation (2003), Hohai University Press: Hohai University Press Nanjing, [in Chinese] |

[37] | Study on hydraulic characteristics of sluice outlet, Eng. J. Wuhan Univ., 1, 43-72 (1974), [in Chinese] |

[38] | Lin, C. A.; Wen, L.; Lu, G.; Wu, Z.; Zhang, J.; Yang, Y.; Zhu, Y.; Tong, L., Real-time forecast of the 2005 and 2007 summer severe floods in the Huaihe River Basin of China, J. Hydrol., 381, 33-41 (2010) |

[39] | Zhao, R., The Xinanjiang model applied in China, J. Hydrol., 135, 371-381 (1992) |

[40] | Nash, J. E.; Sutcliffe, J. V., River flow forecasting through conceptual model, J. Hydrol., 10, 282-290 (1970) |

[41] | Yu, B.; Ni, J.; Yang, X.; Ben, P., Research on hydrodynamic numerical model for main stream of Huaihe River from Fushan to outlet of Hongze lake, Water Resour, Hydr. Eng., 42, 38-42 (2011), in Chinese |

[42] | Bates, P. D.; Wilson, M. D.; Horritt, M. S.; Mason, D. C.; Holden, N.; Currie, A., Reach scale floodplain inundation dynamics observed using airborne synthetic aperture radar imagery: Data analysis and modelling, J. Hydrol., 328, 306-318 (2006) |

[43] | United States Geological Survey (USGS), Landsat 5 TM image for the Hongze Lake. Available at: http://www.usgs.gov/, 2007 (accessed 26 March 2019). |

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