考虑下渗的一维河道水流数学模型
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摘要
采用Green-Ampt下渗模型描述河道下渗,基于完整圣维南方程建立一维河道水流数学模型.为准确求解控制方程解中可能包含的激波与间断,采用有限体积法离散控制方程,使用具有总变差最小特性的SLIC数值格式求解通量.对坡面产流实验进行模拟从而验证模型.应用该模型对浊漳河西南源2场典型场次洪水进行数值模拟,计算结果和实测流量过程吻合良好,而传统不考虑下渗的水流数学模型计算结果与实测数据差异较大,表明该模型能更好地反映强烈下渗条件下洪水演进实际情况.对模型参数进行敏感性分析,计算结果显示糙率、Green-Ampt压力水头以及前期土湿对计算结果均有一定影响.该模型相较传统模型能准确模拟干旱和半干旱地区河道洪水演进的过程,具有推广应用价值.
A one-dimensional hydrodynamic model for open channel flow considering infiltration is established based on the traditional Saint-Venant equations, with the soil infiltration described by the Green-Ampt equation. The governing equations are discretized by the finite volume method and numerical fluxes are estimated by the total-variation-diminishing(TVD) version of the slope limiter centered(SLIC) scheme, which can automatically capture shock waves and discontinuities featured by hyperbolic equations. The proposed model is first validated against an experimental test case. Then the model is applied to resolve two observed flash floods in the Zhuozhang River in Shanxi Province, China. The results obtained by the present model agree well with the field observed datasets, compared to their counterparts by the traditional model. Sensitivity analyses of the model parameters demonstrate that the discharge hydrographs are sensitive to the Manning roughness and the parameters in the Green-Ampt equation. Finally, the proposed model incorporating infiltration is shown to be essential for the correct prediction of river flood routing in arid and semi-arid areas, which dictates the value of the present model in practical applications.
A one-dimensional hydrodynamic model for open channel flow considering infiltration is established based on the traditional Saint-Venant equations, with the soil infiltration described by the Green-Ampt equation. The governing equations are discretized by the finite volume method and numerical fluxes are estimated by the total-variation-diminishing(TVD) version of the slope limiter centered(SLIC) scheme, which can automatically capture shock waves and discontinuities featured by hyperbolic equations. The proposed model is first validated against an experimental test case. Then the model is applied to resolve two observed flash floods in the Zhuozhang River in Shanxi Province, China. The results obtained by the present model agree well with the field observed datasets, compared to their counterparts by the traditional model. Sensitivity analyses of the model parameters demonstrate that the discharge hydrographs are sensitive to the Manning roughness and the parameters in the Green-Ampt equation. Finally, the proposed model incorporating infiltration is shown to be essential for the correct prediction of river flood routing in arid and semi-arid areas, which dictates the value of the present model in practical applications.
引文
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[11] Lima J L M P.Model kininf for overland flow on pervious surface[M].Overland Flow:Hydraulics and Erosion Mechanics,2001.
[12] Mlv M,Todini E,Libralon A.A Bayesian decision approach to rainfall thresholds based flood warning[J].Hydrology & Earth System Sciences Discussions,2005,2(6):413-426.
[2] Morin E,Grodek T,Dahan O,et al.Flood routing and alluvial aquifer recharge along the ephemeral arid Kuiseb River,Namibia[J].Journal of Hydrology,2009,368(1):262-275.
[3] Costa A C,Bronstert A,Araújo J C D.A channel transmission losses model for different dryland rivers[J].Hydrology & Earth System Sciences,2011,16(4):1111-1135.
[4] Hutton C J,Brazier R E,Nicholas A P,et al.On the effects of improved cross‐section representation in one‐dimensional flow routing models applied to ephemeral rivers[J].Water Resources Research,2012,48(4):4509.
[5] Noorduijn S L,Shanafield M,Trigg M A,et al.Estimating seepage flux from ephemeral stream channels using surface water and groundwater level data[J].Water Resources Research,2014,50(2):1474-1489.
[6] Cheng Liang,Wang Zongzhi,Hu Siyi,et al.Flood routing model incorporating intensive streambed infiltration[J].Science China Earth Sciences,2015,58(5):718-726.
[7] Cao Zhixian,Meng Jian,Pender G,et al.Flow resis tance and momentum flux in compound open channels[J].Journal of Hydraulic Engineering,2006,132(12):1272-1282.
[8] 朱昊宇,段晓辉.Green-Ampt入渗模型国外研究进展[J].中国农村水利水电,2017,(10):6-12.Zhu Haoyu,Duan Xiaohui.Research progress of Green-Ampt soil water infiltration model in foreign countries[J].China Rural Water & Hydropower,2017,(10):6-12.
[9] Toro E F.Shock-capturing methods for free-surface shallow flows[M].Chichester :John Wiley,2001.
[10] Huang Wei,Cao Zhixian,Qi Wenjun,et al.Full 2D hydrodynamic modelling of rainfall-induced flash floods[J].Journal of Mountain Science,2015,12(5):1203-1218.
[11] Lima J L M P.Model kininf for overland flow on pervious surface[M].Overland Flow:Hydraulics and Erosion Mechanics,2001.
[12] Mlv M,Todini E,Libralon A.A Bayesian decision approach to rainfall thresholds based flood warning[J].Hydrology & Earth System Sciences Discussions,2005,2(6):413-426.