摘要
我国已建成各类型水库8.7万余座,大坝数量居世界首位。水库大坝在防洪、供水、发电、灌溉等方面发挥了巨大的社会经济效益。然而我国病险水库多且分布广,其溃决已成为国家防灾减灾工作中的一个突出问题。针对溃坝灾害仍然频频发生、防洪形势十分严峻的现状,开展溃坝洪水数学模型研究,建立大坝溃决致灾过程预报理论与方法体系,对保障防洪安全、经济安全和生态安全具有十分重要的现实意义。复杂计算域和地形条件下溃坝洪水演进高性能数值模型研究一直是国内外学术界和工程界关注的前沿研究领域之一。然而,我国在溃坝洪水数值模拟技术方面的研究还很不系统和深入,难以为大坝安全管理提供有效的决策支持,这与我国大坝数量、病险比例、险情发生的高频率和溃决后果的严重性很不相称,因此,亟需在溃坝洪水数值模拟方面进行深入研究并取得突破,建立一套高效、稳定、可靠的溃坝洪水数学模型,揭示复杂条件下溃坝洪水的水动力学特性,为建立我国坝堤溃决风险分析与灾害评估系统提供理论和技术基础,为政府部门做出正确的防灾减灾决策提供科学依据。
本文以溃坝洪水为研究对象,基于二维浅水方程和Godunov型有限体积法,建立了适用于不规则计算域和地形上溃坝洪水演进的高性能二维数学模型,分析了溃坝洪水的水动力学特性,并以漳河水库和荆江分洪区为研究区域分别进行了洪水分析,相关研究成果已应用于973项目的工程应用示范中。本文主要研究工作和创新点包括：
(1)提出了二维浅水方程的一种改进形式。基于三维Navier-Stokes方程推导出传统二维浅水方程,从理论上详细论述了由于使用传统二维浅水方程导致基于斜底三角单元和中心型底坡项近似方法的数值模型需要构造动量通量校正项的问题,并进一步阐明了所构造的动量通量校正项可能引起的计算失稳问题,进而针对上述问题提出了二维浅水方程的一种改进形式。
(2)建立了适用于不规则计算域和地形上溃坝洪水演进的高性能二维数学模型。模型的特色和创新包括地形表达具有二阶精度,在不使用任何通量校正项的前提下模型具有和谐性,可准确模拟缓流、急流、混合流、间断流等复杂流态问题,可在固定网格上有效模拟干湿动边界问题等。
(3)首次从理论上分析了基于两步显式Runge-Kutta法处理摩阻项时面临的刚性问题,并采用一种半隐式格式处理摩阻项。该半隐式格式能保证不改变流速分量的方向,可使与小水深有关的大流速降低至合理范围,有利于计算稳定。
(4)运用一系列经典测试算例对模型进行系统地验证。计算结果表明,模型具有和谐性、水量守恒性、较高的计算精度、复杂混合流态处理能力、高分辨率激波捕获能力、不规则地形处理能力、复杂边界拟合能力、计算稳定性等优点。
(5)分析了河道坡降、河道阻力、下游河道初始状态、坝前水位、入库流量和溃口宽度等因素对溃坝洪水传播过程中溃口洪峰流量以及下游断面洪水到达时间、洪峰流量、最大淹没水深等方面的影响。
(6)分析了梯级坝溃决的洪水增强效应。结果表明,上游的溃坝洪水演进到下游水库后,会在下游库区及坝前产生叠加效应,造成水位峰值的升高,并进一步影响下游坝后河道的水位、流量过程及流态。
(7)利用水动力学模型对漳河水库和荆江分洪区进行了洪水分析,给出了最大淹没水深、最大流速、最大单宽流量、洪水到达时间、最大淹没水深到达时间等洪水风险专题图。
There are about 87,000 reservoirs currently in China. Reservoirs have played an important role in flood control, water supply, hydropower generation, irrigation, etc. Howervr, there are many dangerous reservoirs in China, and the dam-break is a critical problem of national disaster prevention and mitigation. According to the present status of frequent dam failure and severe flood control situation, it is vital to carry out research into mathatical model of dam-break floods, and to develop the theory and method system on dam-break disaster prediction. High-performance numerical model for dam-break floods simulation with complex geometry and topography is always a frontier research field in academic and engineering circles. However, there is an overall lack of systemic and deep research on the dam-break floods simulation in China. To provide a theoretical and technical foundation for constructing the system of dam-break risk analysis and disaster evaluation, as well as to provide scientific basis for government to make an appropriate dicision in disaster prevention and mitigation, it is necessary to develop a high-performance mathematical model of dam-break floods, and to analyse the hydrodynamic characteristics of dam-break floods.
In this thesis, a high-performance two-dimensional mathematical model for dam-break floods over complex topography and irregular domain is developed, and the hydrodynamic characteristics of dam-break floods is analysed by some ideal dam-break problems. Besides, the proposed model is used in Zhang River reservoir and Jingjiang flood diversion area for flood risk analysis. The main work and innovation includes:
(1) A new formulation of the SWEs is presented as the basis of a well-balanced Godunov-type finite volume scheme. In the framework of sloping bottom model, the need for momentum flux corrections to preserve C-property is revealed theoretically when the bed slope terms are approximated directly. At the same time, the potential problem result from the corrections is mathematically analysed.
(2) A high-performance, two-dimensional mathematical model for dam-break floods simulation with complex domain and topography is developed. The proposed model has some advantages including modeling terrain with second-order accuracy, preserving the well-balanced property without any momentum flux corrections, accurately predicting all flow regimes (subcritical, supercritical, transcritical, discontinuities, etc.), and effectively reproducing the wetting and drying processes over irregular terrain on fixed meshed.
(3) The potential stiff problem of two step explicit Runge-Kutta method for friction term treatment is theoretically analysed, and a semi-implicit scheme is used to deal with the stiff problem. The semi-implicit scheme not only preserves the direction of velocity component, but also greatly reduces a large velocity to a reasonable value when the water depth is very small, which is beneficial to model stability.
(4) The proposed model is validated by a set of benchmarks, including ideal test cases with theoretical solutions, laboratory experiments with measured datas, and so on. Results show that the porposed model is accurate, well-balanced and mass conservative, and has the ability to simulate complex flow and to capture shocks with high-resolution.
(5) The influence of bed slope, friction, initial states, inflow and width of dam-breach on peak discharge, elapsed time until arrival of flood, maximum water depth is analysed.
(6) The enhancement effect due to cascade reservoirs failure is simulated. Numerical results show that dam-break floods results from upstream reservoir would make an additive effect at the downstream dam site, increase the peak value of water level, and further influence the flood routine in the downstream river.
(7) The proposed dam-break floods model is used for flood analysis in Zhang River reservoir and Jingjiang flood diversion area, and some special flood risk maps based on computational grids are presented, including maximum water depth, maximum velocity, maximum unit discharge per length, elapsed time until arrival of flood, and elapsed time until arrival of maximum water depth.
引文
[1]南京水利科学研究院.国家重点基础研究发展计划课题“土石坝-水库耦合系统动力学机理”课题总结报告,2011年9月.
[2]Singh V. P. Dam breach modeling technology. Dordrecht, The Netherlands:Kluwer academic publisher,1996.
[3]Baecher G. B., Pate M. E., Neufville R. D. Risk of dam failure in benefit cost analysis. Water Resources Research,1980,16(3):449-456.
[4]Morris M. W. CADAM:Concerted Action on Dambreak Modeling-Final Report. Report SR 571, Jan.2000.
[5]Morris M. W. IMPACT:Investigation of Extreme Flood Processes and Uncertainty-Final Technical Report. Jan.2005.
[6]International Commision on Large Dams (ICOLD) Bulletin 111. Dam-break flood analysis,1998.
[7]中华人民共和国水利部.SL 164-2010溃坝洪水模拟技术规程.北京：人民出版社,2010.
[8]Saint-Venant A. J. C. Theorie du mouvement non-permanent des eaus, avec application aux crues des rivieres et a l'introduction des marees dans leur lit. Compte-Rendu a 1'Academie des Sciences de Paris,1871,73:147-154.
[9]Ritter A. Die fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure,1892,36(33):947-954.
[10]Dressler R. F. Hydraulic resistance effect upon the dam-break functions. Journal of Research of the National Bureau of Standards,1952,49(3):217-225.
[11]Dressler R. F. Unsteady non-linear waves in sloping channels. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,1958, 247(1249):186-198.
[12]Su S.-T., Barnes A. H. Geometric and frictional effects on sudden releases. ASCE Journal of the Hydraulics Division,1970,96(11):2185-2200.
[13]Stoker J. J. Water waves. Wiley, New York:Interscience Publishers,1957.
[14]Ancey C., Iverson R. M., Rentschler M., et al. An exact solution for ideal dam-break floods on steep slopes. Water Resources Research,2008,44(1): W01430.
[15]Sampson J., Easton A., Singh M. Moving boundary shallow water flow above parabolic bottom topography. ANZIAM Journal,2006,47(EMAC2005): C373-C387.
[16]Thacker W. C. Some exact solutions to the nonlinear shallow-water wave equations. Journal of Fluid Mechanics,1981,107:499-508.
[17]Wu C., Huang G, Zheng Y. Theoretical solution of dam-break shock wave. ASCE Journal of Hydraulic Engineering,1999,125(11):1210-1215.
[18]王船海,李光炽.实用河网水流计算.南京：河海大学出版社,2000.
[19]Chen C., Armbruster J. T. Dam-break wave model:formulation and verification. ASCE Journal of the Hydraulics Division,1980,106(5):747-767.
[20]Hunt B. Dam-break solution. ASCE Journal of Hydraulic Engineering,1984, 110(6):675-686.
[21]Hunt B. An inviscid dam-break solution. IAHR Journal of Hydraulic Research, 1987,25(3):313-327.
[22]Hunt B. Asymptotic solution for dam-break problem. ASCE Journal of the Hydraulics Division,1982,108(1):115-126.
[23]林秉南,龚振瀛,王连祥.突泄坝址过程线简化分析.清华大学学报(自然科学版),1980,20(1)：17-31.
[24]谢任之.溃坝坝址流量计算.水利水运科学研究,1982,(1)：43-58.
[25]伍超,吴持恭.求解任意决口断面溃坝水力特性的形态参数分离法.水利学报, 1988,(9)：10-18.
[26]谭振宏.平底棱柱体水库溃坝波分析.水利学报,1992,(4)：39-47.
[27]王立辉,胡四一.溃坝问题研究综述.水利水电科技进展,2007,27(1)：80-85.
[28]文岑,蒋友祥,赵海燕.溃坝问题数值模拟研究综述.中国科技信息,2010,(21)：58-61.
[29]张大伟.堤坝溃决水流数学模型及其应用研究[博士学位论文].北京：清华大学水利水电工程系,2008.
[30]李义天,赵明登,曹志芳.河道平面二维水沙数学模型.北京：中国水利水电出版社,2002.
[31]Katopodes N. D., Strelkoff T. Computing two-dimensional dam-break flood waves. ASCE Journal of the Hydraulics Division,1978,104(9):1269-1288.
[32]Katopodes N. D., Strelkoff T. Two-dimensional shallow water-wave models. ASCE Journal of the Engineering Mechanics Division,1979,105(2):317-334.
[33]Chanson H. Applications of the Saint-Venant equations and method of characteristics to the dam break wave problem. Australia:Dept. of Civil Engineering, The University of Queensland. Report No. CH55/05, May 2005.
[34]Chanson H. Application of the method of characteristics to the dam break wave problem. IAHR Journal of Hydraulic Research,2009,47(1):41-49.
[35]Courant R., Friedrichs K., Lewy H. On the partial difference equations of mathematical physics. Mathematische Annalen,1928,100:32-74.
[36]江绍刚.潮流数值计算ADI方法的研究.海洋科学,1988,(4)：12-16.
[37]张华庆,陆永军,华祖林.拟合坐标下河道二维非恒定流计算.水道港口,1992,(3)：1-8.
[38]徐峰俊,刘俊勇.伶仃洋海区二维不平衡非均匀输沙数学模型.水利学报,2003,(7)：16-21,29.
[39]Toro E. F. Riemann solvers and numerical methods for fluid dynamics. Berlin: Springer,1997.
[40]Turan B. Numerical solutions to dam break wave propagation. World Environmental and Water Resources Congress 2008:Ahupua'A, pp.1-9,2008.
[41]Nujic M. Efficient implementation of non-oscillatory schemes for the computation of free surface flows. IAHR Journal of Hydraulic Research,1995,33(1):101-111.
[42]Louaked M., Hanich L. TVD scheme for the shallow water equations. IAHR Journal of Hydraulic Research,1998,36(3):363-378.
[43]Rahman M., Hanif Chaudhry M. Computation of flow in open-channel transitions. IAHR Journal of Hydraulic Research,1997,35(2):243-256.
[44]Han K.-Y., Lee J.-T., Park J.-H. Flood inundation analysis resulting from levee-break. IAHR Journal of Hydraulic Research,1998,36(5):747-759.
[45]Lie I. Well-posed transparent boundary conditions for the shallow water equations. Applied Numerical Mathematics,2001,38(4):445-474.
[46]Baghlani A., Talebbeydokhti N., Abedini M. J. A shock-capturing model based on flux-vector splitting method in boundary-fitted curvilinear coordinates. Applied Mathematical Modelling,2008,32(3):249-266.
[47]Reggio M., Hess A., Ilinca A.3-D Multiple-level simulation of free surface flows. IAHR Journal of Hydraulic Research,2002,40(4):413-423.
[48]Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics,1981,43(2):357-372.
[49]Osher S, Solomon F. Upwind difference schemes for hyperbolic conservation laws. Mathematics of Computation,1982,38(158):339-374.
[50]Harten A., Lax P. D., Van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation-laws. SIAM Review,1983,25(1):35-61.
[51]Godunov S. K. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Matematicheskii Sbornik,1959,47: 271-306.
[52]Alcrudo F., Garcia-Navarro P. Flux difference splitting for 1D open channel flow equations. International Journal for Numerical Methods in Fluids,1992,14(9): 1009-1018.
[53]Garcia-Navarro P., Alcrudo F., Saviron J. M.1-D open-channel flow simulation using TVD MacCormack scheme. ASCE Journal of Hydraulic Engineering,1992, 118(10):1359-1372.
[54]Glaister P. Prediction of supercritical flow in open channels. Computers & Mathematics with Applications,1992,24(7):69-75.
[55]Alcrudo F., Garcia-Navarro P. A high resolution Godunov-type scheme in finite volumes for the 2D shallow water equations. International Journal for Numerical Methods in Fluids,1993,16(6):489-505.
[56]戴阳豪,张华庆,张征.三角形网格的自动生成及其局部加密技术研究.水道港口,2012,33(1)：77-81.
[57]Song L., Zhou J., Guo J., et al. A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain. Advances in Water Resources,2011,34(7):915-932.
[58]Begnudelli L., Sanders B. F. Unstructured grid finite-volume algorithm for shallow-water flow and scalar transport with wetting and drying. ASCE Journal of Hydraulic Engineering,2006,132(4):371-384.
[59]Song L., Zhou J., Li Q., et al. An unstructured finite volume model for dam-break floods with wet/dry fronts over complex topography. International Journal for Numerical Methods in Fluids,2011,67(8):960-980.
[60]Yoon T. H., Kang S. K. Finite volume model for two-dimensional shallow water flows on unstructured grids. ASCE Journal of Hydraulic Engineering,2004,130(7): 678-688.
[61]Zhao D. H., Shen H. W., Lai J. S., et al. Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling. ASCE Journal of Hydraulic Engineering,1996, 122(12):692-702.
[62]宋利祥,周建中,王光谦,等.溃坝水流数值计算的非结构有限体积模型.水科学进展,2011,22(3)：373-381.
[63]宋利祥,周建中,郭俊,等.复杂地形上坝堤溃决洪水演进的非结构有限体积模型.应用基础与工程科学学报,2012,20(1)：149-158.
[64]岳志远,曹志先,李有为,等.基于非结构网格的非恒定浅水二维有限体积数学模型研究.水动力学研究与进展A辑,2011,26(3)：359-367.
[65]夏军强,王光谦,Lin B.-L.,等.复杂边界及实际地形上溃坝洪水流动过程模拟.水科学进展,2010,21(3)：289-298.
[66]艾丛芳,金生.基于非结构网格求解二维浅水方程的高精度有限体积方法.计算力学学报,2009,26(6)：900-905.
[67]潘存鸿.三角形网格下求解二维浅水方程的和谐Godunov格式.水科学进展,2007,18(2)：204-209.
[68]王鑫,曹志先,岳志远.强不规则地形上浅水二维流动的数值计算研究.水动力学研究与进展A辑,2009,24(1)：56-62.
[69]Liang Q., Borthwick A. G. L. Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Computers & Fluids,2009,38(2): 221-234.
[70]Liang Q., Marche F. Numerical resolution of well-balanced shallow water equations with complex source terms. Advances in Water Resources,2009,32(6): 873-884.
[71]张大伟,王兴奎,李丹勋.建筑物影响下的堤坝溃决水流数值模拟方法.水动力学研究与进展A辑,2008,23(1)：48-54.
[72]王志力,耿艳芬,金生.具有复杂计算域和地形的二维浅水流动数值模拟.水利学报,2005,36(4)：439-444.
[73]Zhao D. H., Shen H. W., Tabios Ⅲ G. Q., et al. Finite-volume two-dimensional unsteady-flow model for river basins. ASCE Journal of Hydraulic Engineering, 1994,120(7):863-883.
[74]George D. L. Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation. Journal of Computational Physics,2008,227(6):3089-3113.
[75]Bermudez A., Vazquez M. E. Upwind methods for hyperbolic conservation laws with source terms. Computer & Fluids,1994,23(8):1049-1071.
[76]LeVeque R. J. Balancing source terms and flux gradients in high-resolution Godunov methods:the quasi-steady wave-propagation algorithm. Journal of Computational Physics,1998,146(1):346-365.
[77]Hubbard M. E., Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. Journal of Computational Physics,2000,165(1): 89-125.
[78]Rogers B. D., Borthwick A. G. L., Taylor P. H. Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver. Journal of Computational Physics,2003,192(2):422-451.
[79]Zhou J. G., Causon D. M., Mingham C. G, et al. The surface gradient method for the treatment of source terms in the shallow-water equations. Journal of Computational Physics,2001,168(1):1-25.
[80]Valiani A., Begnudelli L. Divergence form for bed slope source term in shallow water equations. ASCE Journal of Hydraulic Engineering,2006,132(7):652-665.
[81]Begnudelli L., Valiani A., Sanders B. F. A balanced treatment of secondary currents, turbulence and dispersion in a depth-integrated hydrodynamic and bed deformation model for channel bends. Advances in Water Resources,2010,33(1):17-33.
[82]Begnudelli L., Sanders B. F., Bradford S. F. Adaptive Godunov-based model for flood simulation. ASCE Journal of Hydraulic Engineering,2008,134(6):714-725.
[83]Begnudelli L., Sanders B. F. Conservative wetting and drying methodology for quadrilateral grid finite-volume models. ASCE Journal of Hydraulic Engineering, 2007,133(3):312-322.
[84]Sanders B. F. Integration of a shallow water model with a local time step. IAHR Journal of Hydraulic Research,2008,46(4):466-475.
[85]Zoppou C., Roberts S. Catastrophic collapse of water supply reservoirs in urban areas. ASCE Journal of Hydraulic Engineering,1999,125(7):686-695.
[86]Valiani A., Caleffi V., Zanni A. Case study:Malpasset dam-break simulation using a two-dimensional finite volume method. ASCE Journal of Hydraulic Engineering, 2002,128(5):460-472.
[87]Liang Q., Borthwick A. G. L., Stelling G. Simulation of dam-and dyke-break hydrodynamics on dynamically adaptive quadtree grids. International Journal for Numerical Methods in Fluids,2004,46(2):127-162.
[88]Aliparast M. Two-dimensional finite volume method for dam-break flow simulation. International Journal of Sediment Research,2009,24(1):99-107.
[89]周雪漪.计算水力学.北京：清华大学出版社,1995.
[90]曹祖德,王运洪.水动力泥沙数值模拟.天津：天津大学出版社,1994.
[91]Hervouet J.-M. Hydrodynamics of free surface flows:modelling with the finite element method. Chichester:John Wiley & Sons,2007.
[92]Flokstra C. The closure problem for depth-averaged two-dimensional flows. In: Proceedings of the 17th congress of the International Association for Hydraulic Research.1977,247-256.
[93]Xia J., Lin B., Falconer R. A., et al. Modelling dam-break flows over mobile beds using a 2D coupled approach. Advances in Water Resources,2010,33(2):171-183.
[94]Guo W.-D., Lai J.-S., Lin G.-F., et al. Finite-volume multi-Stage scheme for advection-diffusion modeling in shallow water flows. Journal of Mechanics,2011, 27(3):415-430.
[95]Babarutsi S., Chu V. H. A two-length-scale model for quasi-two-dimensional turbulent shear flows. In:Proceedings of the 24th congress of the IAHR, vol. C, Madrid, Spain. International Association for Hydraulic Research,1991,51-60.
[96]Rastogi A. K., Rodi W. Predictions of heat and mass-transfer in open channels. Jouranl Hydraulic Division,1978,104(3):397-420.
[97]孙东坡,廖小龙,王鹏涛,等.河道生产堤对洪水影响的二维数值模拟研究.水动力学研究与进展A辑,2007,22(1)：24-30.
[98]万洪涛,周成虎,吴应湘,等.黄河下游花园口-夹河滩河段二维洪水模拟.水科学进展,2002,13(2)：215-222.
[99]胡晓张,张小峰,何用,等.含生产堤等线状建筑物的蓄洪区水流数值模拟.人民珠江,2007,(5)：21-24,42.
[100]杨学斌.波、流联合作用下二维水流、泥沙数学模型研究[硕士学位论文].天津：天津大学建筑工程学院,2008.
[101]Toro E. F. Shock-capturing methods for free-surface shallow flows. Chichester: John Wiley & Sons,2001.
[102]LeVeque R. J. Finite volume methods for hyperbolic problems. Cambridge: Cambridge University Press,2002.
[103]Zia A., Banihashemi M. A. Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds. International Journal for Numerical Methods in Fluids,2008,56(11):2021-2043.
[104]Fraccarollo L., Toro E. F. Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. IAHR Journal of Hydraulic Research,1995,33(6):843-864.
[105]Einfeldt B. On Godunov-type methods for gas dynamics. SIAM Journal on Numerical Analysis,1988,25(2):294-318.
[106]Einfeldt B., Munz C. D., Roe P. L., et al. On Godunov-type methods for near low densities. Journal of Computational Physics,1991,92(2):273-295.
[107]Aureli F., Maranzoni A., Mignosa P., et al. A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography. Advances in Water Resources,2008,31(7):962-974.
[108]Canestrelli A., Dumbser M., Siviglia A., et al. Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed. Advances in Water Resources,2010,33(3):291-303.
[109]Hubbard M. E. Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids. Journal of Computational Physics,1999,155(1): 54-74.
[110]Van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. Journal of Computational Physics,1979, 32(1):101-136.
[111]Anastasiou K., Chan C. T. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. International Journal for Numerical Methods in Fluids,1997,24(11):1225-1245.
[112]Harten A., Engquist B., Osher S., et al. Some results on uniformly high order accurate essentially non-oscillatory schemes. Applied Numerical Mathematics, 1986,2(3-5):347-377.
[113]Liu X. D., Osher S., Chan T. Weighted essentially nonoscillatory schemes. Journal of Computational Physics,1994,115(1):200-212.
[114]李庆扬,王能超,易大义.数值分析(第5版).北京：清华大学出版社,2008.
[115]Wylie E. B., Streeter V. L. Fluid transients in systems. Englewood Cliffs, N.J.: Prentice-Hall,1993.
[116]Begnudelli L., Sanders B. F. Simulation of the St. Francis dam-break flood. ASCE Journal of Engineering Mechanics,2007,133(11):1200-1212.
[117]Gallegos H. A., Schubert J. E., Sanders B. F. Two-dimensional, high-resolution modeling of urban dam-break flooding:a case study of Baldwin Hills, California. Advances in Water Resources,2009,32(8):1323-1335.
[118]Berthon C. Why the MUSCL-Hancock scheme is L1-stable. Numerische Mathematik,2006,104(1):27-46.
[119]Bernetti R., Titarev V. A., Toro E. F. Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. Journal of Computational Physics,2008,227(6):3212-3243.
[120]Goutal N., Maurel F., (Eds). Proceedings of the 2nd Workshop on Dam-Break Wave Simulation, Chatou, France,1997, EDF/DER HE-43/97/016/B.
[121]Vazquez-Cendon M. E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. Journal of Computational Physics,1999,148(2):497-526.
[122]Gallouet T., Herard J. M., Seguin N. Some approximate Godunov schemes to compute shallow-water equations with topography. Computers & Fluids,2003, 32(4):479-513.
[123]Kesserwani G, Liang Q. Well-balanced RKDG2 solutions to the shallow water equations over irregular domains with wetting and drying. Computers & Fluids, 2010,39(10):2040-2050.
[124]Xing Y, Zhang X., Shu C.-W. Positivity-preserving high-order well-balanced discontinuous Galerkin methods for the shallow water equations. Advances in Water Resources,2010,33(12):1476-1493.
[125]Aureli F., Mignosa P., Tomirotti M. Dam-break flows in presence of abrupt bottom variations. In:Proc.ⅩⅩⅧ IAHR Congr., Graz, Austria,1999,163-171.
[126]Kesserwani G., Liang Q. Locally limited and fully conserved RKDG2 shallow water solutions with wetting and drying. Journal of Scientific Computing,2012, 50(1):120-144.
[127]Caleffi V., Valiani A., Zanni A. Finite volume method for simulating extreme flood events in natural channels. IAHR Journal of Hydraulic Research,2003,41(2): 167-177.
[128]Wang J. W., Liu R. X. A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems. Mathematics and Computers in Simulation,2000,53(3):171-184.
[129]Singh J., Altinakar M. S., Ding Y. Two-dimensional numerical modeling of dam-break flows over natural terrain using a central explicit scheme. Advances in Water Resources,2011,34(10):1366-1375.
[130]Gottardi G, Venutelli M. Central scheme for two-dimensional dam-break flow simulation. Advances in Water Resources,2004,27(3):259-268.
[131]Brufau P., Garcia-Navarro P. Two-dimensional dam break flow simulation. International Journal for Numerical Methods in Fluids,2000,33(1):35-57.
[132]Soares Frazao S., Zech Y. Dam Break in channels with 90° bend. ASCE Journal of Hydraulic Engineering,2002,128(11):956-968.
[133]Brufau P., Vazquez-Cendon M. E., Garcia-Navarro P. A numerical model for the flooding and drying of irregular domains. International Journal for Numerical Methods in Fluids,2002,39(3):247-275.
[134]Brufau P., Garcia-Navarro P. Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique. Journal of Computational Physics,2003,186(2):503-526.
[135]Bellos C. V., Soulis J. V., Sakkas J. G Experimental investigation of two-dimensional dam-break induced flows. IAHR Journal of Hydraulic Research, 1992,30(1):47-63.
[136]Liang Q. Flood simulation using a well-balanced shallow flow model. ASCE Journal of Hydraulic Engineering,2010,136(9):669-675.
[137]中国水利水电科学研究院.湖北省洪水风险区规划及示范工程洪水风险图编 制技术设计报告,2008年5月.
[138]湖北省水利水电规划勘测设计院.湖北省水利重点科研项目“溃坝及其风险范围的研究”综合报告,2011年4月.
[139]Morris M. Breaching processes:A state of the art review. FLOODsite Project Report T06-06-03. FLOODsite,2009.