浅水间断流动数值模拟及其在钱塘江河口涌潮分析中的应用
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
涌潮、水跃、溃坝波、浅水变形后的波浪、闸门突然开启形成的涌波等浅水间断流动的数值模拟具有很高的学术价值和实际应用价值,一直是计算水动力学的热点和难点之一。
     本文在分析钱塘江涌潮和浅水流动方程基本性质的基础上,分别应用Godunov格式和KFVS(Kinetic Flux Vector Splitting)格式建立了一、二维浅水间断流动数值模型,应用WLTF(Water Level-bottom Topography Formulation)方法结合源项离散技术解决了守恒型计算格式的“和谐”性,应用改进的干底Riemann解处理动边界问题。模型在典型算例验证的基础上,模拟了钱塘江涌潮传播过程以及涌潮作用下的泥沙输移。本文的主要工作如下:
     (1)应用基于准确Riemann解的Godunov格式建立了一、二维浅水间断流动数值模型。为保证方程左边的压力项与方程右边底坡源项始终保持“和谐”,求解法向通量过程中采用了WLTF方法,同时对压力项和底坡源项采用相同的离散方法。对于三角形网格,采用两种方法达到计算格式的“和谐”,第一种方法底坡源项采用静水压力原理变换离散,第二种方法采用变换控制方程来实现模型的和谐。应用类似于MUSCLE方法,建立了三角形网格下二阶精度计算格式。
     (2)应用宏观和微观变量基本关系式,以平衡态的Boltzmann方程为基础,导出了基于Boltzmann方程的一维和二维浅水流动方程。应用有限体积法离散浅水流动方程,法向数值通量采用KFVS格式求解,建立了具有空间二阶精度的一维和二维浅水流动方程的KFVS格式。为保证计算格式的和谐性,除采用WLTF方法外,通量计算中考虑了底坡源项的作用。
     (3)钱塘江河口存在大片滩地,动边界处理好坏对涌潮计算结果有很大影响。本文应用改进的干底Riemann解处理动边界问题。根据WLTF思想,将经典干底Riemann解仅适用于平底情形进行了改进,使其能应用到非平底的情况。数值试验结果表明,该方法能模拟动边界条件下大梯度流动问题。
     (4)上述建立的基于Godunov格式和KFVS格式的两个二维数值模型在多个典型算例验证的基础上,模拟了钱塘江涌潮的形成、发展和衰减的过程,复演了交叉潮、一线潮和回头潮等潮景。经实测资料验证,计算结果反映了涌潮到达时刻潮位暴涨、流速迅速从落潮转为涨潮并达到极值的现象,解决了以前计算模型潮位涨幅偏小、涌潮流速大大偏小以及流量不守恒等问题。
     (5)在水流数值模型的基础上,应用Godunov格式建立了三角形网格下具有空间二阶精度的二维泥沙输移数值模型,模拟了钱塘江涌潮作用下泥沙输移规律,复演了涌潮前后含沙量突变的过程。计算结果表明涌潮对泥沙输移、河床演变有着深刻的影响,并揭示了钱塘江河口高含沙量区的成因、洪冲潮淤以及大冲大淤的机理。
Numerical simulation of discontinuous shallow water flows, such as tidal bores, hydraulic jumps, dam-break waves, waves distorted due to shallow water, surge wave formed by suddenly-opened sluice, etc. is of great academic and practical significance, and thus has long been a hotspot and difficult issue in computational hydrodynamics.
     In this thesis, based on the analyses of basic characteristics of the tidal bores on the Qiantang River and of the related shallow water equations, 1D and 2D mathematical models were developed for simulating discontinuous shallow water flow by using the Godunov scheme and KFVS (Kinetic Flux Vector Splitting) scheme, in which the well-balanced problem of conservative computational schemes was solved by applying the WLTF(Water Level-bottom Topography Formulation) combined with the discretization technique for treating the source term generated by uneven bottom topography, and the wet/dry technique was invoked to improve the Riemann solution for the dry bed. On the basis of the verification of the above models by simulating typical examples, the models were employed to compute the propagation of the tidal bore on the Qiantang River and the sediment transportation under the effect of the tidal bore.
     The main results in this thesis are as follows.
     (1) The 1D and 2D mathematical models were established for simulating the discontinuous shallow water flow by using the Godunov scheme. In order to keep the well-balance between the pressure term on the left-hand side and the source term due to bottom topography on the right-hand side of the shallow water equations (SWE), the WLTF was applied in the process of solving the normal numerical flux, and the same discretization method was used for both the pressure term and the source terms. With the triangular grids, two methods were proposed to keep the models well-balanced. Firstly, the source term due to bottom topography was discretize by using hydrostatic pressure law. Secondly, the governing equations were transformed to reach the well-balance. With a technique similar to the MUSCLE, a 2nd-order accuracy scheme in space with triangular grids was developed.
     (2) Based on the Boltzmann equation for the equilibrium state, the 1D and 2D shallow water equations were derived from the basic relationship between macroscopic and microcosmic variables. The 1D and 2D KFVS schemes for solving the SWE were developed with the 2nd-order accuracy in space by using the finite volume method (FVM) to discretize the SWE and the KFVS method to compute normal numerical flux. In order to keep the scheme well-balanced, in addition to the WLTF, the effect of the source term due to bottom topography was considered in the computation of normal numerical flux.
     (3) There are extensive shoals at the Qiantang estuary, so the wet/dry technique has great impact on the computed results for the tidal bore. In this thesis, an improved Riemann solution on dry bed was proposed to deal with moving boundary. According to the idea of WLTF, the classical Riemann solution on dry bed only applicable to even bottoms was improved to be applied to uneven bottom. Numerical tests show that the method can be applied to simulate discontinuous flow in the condition of moving boundary.
     (4) The above two 2D mathematical models with the Godunov scheme and KFVS scheme were validated by some typical tests, and then employed to simulate the formation, evolution and dissipation of the tidal bore at the Qiantang estuary, and to replicate some bore sceneries, such as the crossed tidal bore, thread-shape bore and returned tidal bore. The computed results were verified by field data, showing the sudden and sharp rise of the tidal level, the rapid velocity conversion from ebb to flood and fast reaching to its extremum during the bore arriving. The models have overcome the problems which appeared in common mathematical models, such as unreasonably smaller water-level rise, velocity increase, and the nonconservatve computed discharge.
     (5) Based on the mathematical model of water flow, a 2D sediment transport mathematical model with the 2nd-order accuracy in space was developed by using the Godunov scheme with triangular grids. The model was used to simulate sediment transport under the tidal bore on the Qiantang River, and to replicate the abrupt variation process of the sediment concentration during the bore arriving. The computed results show that the tidal bore has great impact on sediment transport and fluvial process, and reveals the cause of formation of high sediment concentration region at the Qiantang estuary, the mechanism of erosion by runoff and deposit by tidal current, and the riverbed variation with large amplitude.
引文
[1] Abbott, M. R., A theory of the propagation of bores in channels and rivers: Proceedings[J], Cambridge Philosophical Society, 1956, 52: 344-362.
    [2] Akanbi A A, Katopodes N D. Model for flood propagation on initially dry land[J]. J. Hydraul. Eng., 1987, 114(15): 689-706.
    [3] Aizinger V, Dawson C. Discontinuous Galerkin methods for two-dimensional flow and transport in shallow water[J], Advances in Water Resources, 2002, 25: 67-84.
    [4] Alcrudo F, Garcia-navarro P, Saviron Jose-Maria. Flux difference splitting for 1D open channel flow equations[J]. Int. J. Numer. Methods in Fluids, 1992, 14: 1009-1018.
    [5] Alcrudo F, Garcia-Navarro P. A high-resolution Godunov-type scheme in finite volumes for 2D shallow-water equations[J]. Int. J. Numer. Methods in Fluids, 1993, 16: 489-505.
    [6] Anastasiou K, Chan CT. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes[J]. Int. J. Numer. Methods in Fluids, 1997, 24(11): 1225-1245.
    [7] Audusse E., Bristeau M. -O.. A well-balanced positivity preserving "second-order" scheme for shallow water flows on unstructured meshes[J], J. Comput. Phys., 2005, 206: 311-333.
    [8] Barnes, F. A., The Trent Eagre: University of Notting-ham[J], 1952, Survey 3, No. 1.
    [9] Bartsch-Winkler and S, Lynch D K. Catalog of worldwide tidal bore occurrences and characteristics[R]. U. S. Geological Survey Circular 1022, 1988, 1-17.
    [10] Bermudez A and Vazquez M. E, Upwind methods for hyperbolic conservation laws with source terms[J], Computers & Fluids, 1994, 23(8): 1049-1071.
    [11] Bermudez A, Dervieux A., Desideri J. A. et al, Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes[J], Comput. Methods Appl. Mech. Eng., 1998, 155(49).
    [12] Branner, J. C., The "pororoca," or bore of the Amazon[J], Science, 1884, 4(95): 488-490.
    [13] Brufau P, Garcia-Navarro P. Two-dimensional dam break flow simulation[J], Int. J. Numer. Methods in Fluids, 2000, 33(1): 35-57.
    [14] Brufau P., Vazquez-Cendon M. E. and Garcia-Navarro P. A numerical model for the flooding and drying of irregular domains[J], Int. J. Numer. Methods in Fluids, 2002, 39: 247-275.
    [15] Brufau P. and Garcia-Navarro P., Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique[J]. J. Comput. Phys., 2003, 186: 503-526.
    [16] Brufau P, Garcia-Navarro P, and Vazquez-Cendon M E, Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography[J], Int. J. Numer. Methods in Fluids, 2004, 45:1047-1082.
    [17] Burguete J and Garcia-Navarro P, Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows[J],Int. J. Numer. Methods in Fluids, 2001, 37:209-248.
    [18] Caputo J.-G. and Stepanyants Y.A., Bore formation, evolution and disintegration into solitons in shallow in shallow inhomogeneous channels[J], Nonlinear Processes in Geophysics, 2003, 10: 407-424.
    [19] Champion, H.H., and Corkan, R.H., The bore in the Trent[J]: Proceedings of the Royal Society of London, Series A, 1936, 154(881):158-180.
    [20] Chang S C. The method of space-time conservation element and solution element——a new approach for solving the Navier Stokes and Euler equations[J]. J. Comput. Phys., 1995, 119:295-324.
    [21] Chang Sin-Chung, Wang Xiao-Yen and Wai-Ming To. Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Convection-Diffusion Problems[J], J. Comput. Phys., 2000, 165: 189-215.
    [22] Chanson H, Mixing and dispersion in tidal bores. a Review[A], Proceedings of International Conference on Estuaries & Coasts, 2003, Hangzhou, China.
    [23] Chanson H, Coastal Observations: The Tidal Bore of the Selune River, Mont Saint Michel Bay, France[J]. Shore & Beach, 2004, 72(4):14-16.
    [24] Chanson H., Physical Modelling of the Flow Field in an Undular Tidal Bore. Journal of Hydraulic Research, 2005a, 43(3):234-244.
    [25] Chanson H., Tidal bore process in the Baie Du Mont Saint Michel(France): Field observations and discussion[A], Proceedings of 31st IAHR Congress, 2005b, p 4037-4046,Seoul, Korea.
    [26] Chitale, S.V., Bores on tidal rivers with special reference to Hooghly[J], Irrigation and Power, 1954,2(1): 110-120.
    [27] Cockburn B, Shu C W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J] . SIAMJ Numer Anal, 1998, 35:2440 - 2463.
    [28] Cockburn, B., Karniadakis, G, Shu, C. W., and Griebel, M., eds., Discontinuous Galerkin methods: Theory, computation and applications (lecture notes in computational science and engineering), 2000, Springer, Berlin.
    [29] Crnjaric-Zic N, Vukovic S, Sopta L, Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations[J], J. Comput. Phys.,2004a, 200: 512-548.
    [30] Crnjaric-Zic N, Vukovic S, Sopta L, Extension of ENO and WENO schemes to one-dimensional sediment transport equations[J], Computers & Fluids, 2004b, 33:31 - 56.
    [31] Deng J Q, Ghidaoui M S. A Boltzmann based mesoscopic model for contaminant transport in flow system[J]. Advances in Water Resources, 2001,24:531-550.
    [32] Dalton, F.K., Fundy's prodigious tides and Petitcodiac's tidal bore[J], Journal of the Royal Astronomical Society of Canada, 1951,45(6): 225-230.
    [33] Dawsonl C,. Westerink J J, Feyen JC and Pothina D, Continuous, discontinuous and coupled discontinuous-continuous Galerkin finite element methods for the shallow water equations[J], Int. J. Numer. Methods in Fluids, 2006, 52:63-88.
    [34] Destriau, Jouanneau, J.M., and Latouche, C, The Gironde estuary[J], Contributions to Sedimentology, 1981, v. 10, 118 p.
    [35] Dong Liyun, Lu W.Z., Leung A.Y.T, Finite volume method on simulating 1D shallow-water flow over uneven bottom[A], WCCMVI in conjunction with APCOM'04[C], Beijing, China, 2004, 300-307.
    [36] Donnelly, Chantal and Chanson, Hubert, Environmental Impact of a Tidal Bore on Tropical Rivers[A]. In 5th International River Management Symposium[C], Queensland, Australia, 2002.
    
    [37] Dracos, TA, Glenne, B.: Stability criteria for open-channel flow[J]. J. Hydr. Div. ASCE,1967,93:79-101.
    [38] Fagherazzi S, Rasetarinera P, Hussaini M. Y, and Furbish D J. Numerical Solution of the Dam-Break Problem with a Discontinuous Galerkin Method[J], J. of Hydraul. Eng., 2004,130(6): 532-539.
    [39] Fraccarollo L, Toro EF. Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problem[J]. J. Hydraul. Res., 1995, 33(6): 843-863.
    [40] Fujihara M, Borthwick AGL. Godunov-Type Solution of Curvilinear Shallow-Water Equations[J]. J. of Hydraul. Eng., 2000, 126(11): 827-836.
    [41] Garcia-Navarro P, Alcrudo F, Saviron JM. 1-D open channel flow simulation using TVD-MacCormack scheme[J]. J. of Hydraul. Eng., 1992, 118:1359-1372.
    [42] Ghidaoui M. S., Deng J. Q., Gray W. G, Xu K. A Boltzmann based model for open channel flows[J]. Int. J. Numer. Methods in Fluids, 2001, 35(4):449-494.
    [43] Giraldo FX, Hesthaven JS, Warburton T. Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations[J]. J. Comput. Phys., 2002, 181:499-525.
    [44] Glaister P. Approximate riemann solutions of the shallow water equations[J]. J. Hydraul. Res., 1988, 26(3): 293-306.
    [45] Greenberg JM, Leroux AY. A well-balanced scheme for the numerical processing of source terms in hyperbolic equations[J], SIAM Journal on Numerical Analysis,1996,33(1):1-16.
    [46] Godunov SK, Finite difference methods for the computation of discontionuous solutions of the equations of fluid dynamics[J], Mat. Sb., 1959, 47:271-306.
    [47] Guinot V and Soares-Frazao S, Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids[J]. Int. J. Numer. Methods in Fluids, 2006, 50:309-345.
    [48] Gurtin ME, On the breaking of water wave on a sloping beach of arbitrary shape[J], Quart.Appl. Math.,1975,v33
    [49] Gusev A.V. and Yu V. Lyapidevskii, Turbulent bore in a supercritical flow over an Irregular bed[J], Fluid Dynamics, 2005, 40(1): 54-61.
    [50] Hager W.H, Schwalt M, Jimenez O and Chaudhry M.H, Supercritical flow near an abrupt wall deflection[J], J. Hydraul. Res., 1994, 32(1): 103-118.
    [51] Harlow F H and Welech J E, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface[J], Phy. Fluids, 1965, 8:2182-2189.
    [52] Harten A. High resolution Schemes for hyperbolic Conservation laws[J]. J. Comput. Phys.,1983,49:357-393.
    [53] Harten A., Lax P. D., and van Leer B., On upstream differencing, differencing and Gudunov-type schemes for hyperbolic conservation-laws[J]. SIAM Rev., 1983, 25(1):35—61.
    [54] Harten A., On high-order accurate interpolation for non-oscillatory shock capturing scheme, in Oscillation Theory[A]. Computation and Methods of Compensated Compactness, C dafermos et al eds. Springer-Verlag, New York, 1986a, 71-105.
    [55] Harten A, Engquist B, Osher S, and Chakravathy R. Some results on uniformly high order accurate essentially non-oscillatory scheme[J]. Applied Numerical Mathematics, 1986b,2:347-377.
    [56] Harten A, Osher S, Uniformly high order accurate essentially non-oscillatory schemes, I [J],SIAM J Numer Ana, 1987a, 24:279-309.
    [57] Harten A, Engquist B, Osher S, and Chakravathy R. Uniformly high order accurate essentially non-oscillatory schemes, III[J], J. Comput. Phys., 1987b, 71:231-303; 1997,131:3-47.
    
    [58] Harten A, ENO schemes with subcell resolution[J]. J. Comput. Phys., 1989, 83:148.
    [59] Hirt C W and Nichols B D, Volume of fluid (VOF) method for the dynamics of free boundaries[J], J. Comput. Phys., 1981, 39:201-225.
    [60] Hou TY and LeFloch P, Why non-conservative scheme converge to the wrong solutions:error analysis[J]. Math. Of Comput., 1994, 62:497-530.
    
    [61] Hu H., Mingham C.G. and Causon D.M., A bore-capturing finite volume method for open-channel flows[J], Int. J. Numer. Methods in Fluids, 1998, 28:1241-1261.
    
    [62] Hubbart M E, Garcia Navarro P. Flux Difference Splitting and the Balancing of Source Terms and Flux Gradients[J]. J. Comput. Phys., 2000, 165:89-125.
    [63] Hui W.H, Computational fluid dynamics for inviscid flows[R], Hong Kong University of Science and Technology, 2001.
    [64] Hui W. H. and Koudriakov S, Computation of the shallow water equations using the unified coordinates[J], SIAM J. Sci. Comput., 2002, 23: 1615-1654.
    [65] Hurlbut G C, Geographical notes[J], Journal of American Geographical Society of New York, 1889, 21: 583-646.
    [66] James H. G., Tidal bore at the mouth of Colorado River December 8 to 10, 1923 [J], Monthly Weather Review, 1924, 98-99.
    [67] Jenny P. and Muller B., Rankine-Hugoniot-Riemann Solver Considering Source Terms and Multidimensional Effects[J], J. Comput. Phys., 1998, 145(1): 575-610.
    [68] Johnson, R. S., A non-linear equation incorporating damping and dispersion[J], J. Fluid Mech., 1970, 42: 49-60.
    [69] Johnson, R. S., Shallow Water Waves on a Viscous Fluid—The Undular Bore[J], The Physics of Fluids, 1972, 15(10): 1693-1699。
    [70] Koch, C and Chanson, An Experimental Study of Tidal Bores and Positive Surges: Hydrodynamics and Turbulence of the Bore Front[R], Department of Civil Engineering, The University of Queensland, 2005.
    [71] Lax PD and Wendroff B, System of conservation laws[J], Comm. Pure Appl. Math., 1960, 13: 217-237.
    [72] LeVeque RJ. Balancing source terms and flux gradients in high-resolution G0dunov methods: the quasi-steady wave-propagation algorithm[J]. J. Comput. Phys., 1998, 146(1): 346-365.
    [73] Lui X-D, Osher S and Chan T, Weighted essentially nonoscillatory schemes[J], J. Comput. Phys., 1994, 115: 200-212.
    [74] Lynch, D. K., 1982, Tidal bores[J], Scientific American, 247(4): 146-156.
    [75] Madsen P. A. and Svendsen I. A., Turbulent bores and hydraulic jumps[J], J. Fluid Mech., 129, 1(1983).
    [76] Mamood K., Yevievich V., Unsteady flow in open channels, Colorado[M], Water Resource Pub. 1975.
    [77] Marshall E, Mendez R. Computational aspects of the random choice method for shallow water equations[J]. J. Comput. Phys., 1981, 39: 1-21.
    [78] Mazumder, N. C., Bose, S., Formation and Propagation of Tidal Bore[J], J. of Waterway Port Coastal and Ocean Engineering, 1995, 12(3): 167-175.
    [79] Mitchell, D. G., Report on tidal measurements in the Petitcodiac River[J], Canadian Hydrographic Service, Tides and Water Levels, Fisheries and Oceans, 1968, v. 2, 29 p.
    [80] Miyata H, Katsumata M, Lee Y G and Kajitani H. A finite-difference simulation method for stronginteractingtwo-layerflow[J]. J. Soc. Naval Archi. Japan, 1988, 163: 1-16.
    [81] Mohammadian A., and Roux D. Y.L. Simulation of shallow flows over variable topographies using unstructured grids[J], Int. J. Numer. Methods in Fluids, 2006,52:473-498.
    [82] Moore,W.u, The Bore of the Tsien-Tang kiang(Hang-Chau Bay) [J], J. China Branch, Royal Asiatic Society, 1888, (23): 185-247.
    [83] Moore,W.u, Further report on the bore of the Tsien-Tang- Kiang[R], London, Potter, Poultry.1893.
    [84] Munchow A., Garvine RW, Nonlinear barotropic tides and bores in estuaries[J], Tellus TELLAL, 1991,43A(3):246-256.
    [85] Nitish C. Mazumder, Probhat K. Chatterjee, and Sunil K. Basak, Generation of Bore[J], J. of Waterway, Port, Coastal and Ocean Engineering, 1984,110(2): 159-170.
    [86] Nitish CM. and Somnath B., Formation of and propagation of tidal bore[J], J. of waterway,port, coastal and ocean engineering, 1995, 121(3): 167-175.
    [87] Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton - Jacobi formulations[J]. J. Comput. Phys., 1988; 79:12 - 49.
    [88] Pan Cunhong, Xu Xuezi, Lin Binyao, Simulation of free surface flow near engineering structures using MAC-method[A], Proceedings of International Conference on Hydrodynamics[C], 1994, Wuxi, China.
    [89] Pan Cunhong, Lin Bingyao, Mao Xianzhong, New development in numerical simulation of the tidal bore[A], Proceedings of the international conference on Estuaries and Coasts[C],Hangzhou, China, 2003, 1:99-114.
    [90] Pan Cunhong, Dai Shiqiang, Chen Senmei, Numerical simulation for 2D shallow water equations by using Godunov-type scheme with unstructured mesh[J], Journal of Hydrodynamics Ser.B, 2006,18(4): 475-480
    
    [91] Partiot H L, Mpmoire sur le mascaret, Paris[R], Dunod, 1861.
    [92] Peregine,D.h., Calculations for the Development of an Undular Bore[J], J. Fluid Mech,1966, 25:321-330.
    [93] Que Yin-Tik and Xu Kun, The numerical study of roll-waves in inclined open channels and solitary wave run-up[J], Int. J. Numer. Methods in Fluids, 2006,50:1003-1027
    [94] Rayleigh Lord, On The Theory of Long Waves and Bores[J], Proceedings of the Royal Society of London, Series A,1914, 90(619):324-328.
    [95] Reed N H, Hill T R. Triangle mesh methods for the Neutron transport equation[R], Los Alamos Scientific Laboratory, Report LAUR-73-479, 1973.
    [96] Roe P L, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes[J],J. Comput. Phys., 1981, 43(2): 357-371.
    [97] Roe P L. Upwind differencing schemes for hyperbolic conservation laws with source terms[A], Proc.First Int.Conf.on Hyperbolic Problems[C]. 1986,41-51.
    [98] Roger B, Fuijhara M, Borthwick AGL. A daptive Q-tree godunov-type scheme for shallow water equations[J]. Int. J. Numer. Methods in Fluids, 2001, 35: 247-280.
    [99] Rowbotham, F.W., 1964, The Severn Bore[M], 2nd edition: Newton-Abbot, North Ponfret, Vt., David & Charles, 104 p.
    [100] Roy, S.C., Inception and propagation of the bore on the Hooghly, in Bagchi[A], K.G., ed., The Bhagirathi-Hooghly Basin: Proceedings of the Interdisciplinary Symposium[C], 1972, p.133-142.
    
    [101] Sanders BF. High-resolution and non-oscillatory solution of the St Venant equations in non-rectangular and non-prismatic channels[J]. J. Hydraul. Res., 2001, 39(3):321-330.
    
    [102] Schonfeld J C, Theoretical considerations on an Experimental Bore[A], IAHR proceedings of the sixth General meeting[C], 1955.
    [103] Schwanenberg D and Harms M, Discontinuous Galerkin Finite-Element Method for Transcritical Two-Dimensional Shallow Water Flows[J], J. of Hydraul. Eng., 2004, 130(5):412-421.
    [104] Sentinelles Petitcodiac Riverkeeper, The Petitcodiac River Tidal Bore 250 Years of Anecdotes[R],2001.
    [105] Shu C-W. High order ENO and WENO schemes[A], in High order methods for computational physics"(Eds: Barth T J and Deconinck H), Lecture Notes in Computational Science and Engineering(9), Springer-Verlag, 1999.
    [106] Simpson J.H., N.R. Fisher and P. Wiles, Reynolds stress and TKE production in an estuary with a tidal bore[J], Estuarine, Coastal and Shelf Science, 60 (2004): 619-627.
    [107] Smolarkiewicz P K, Margolin L G. MPDATA: A finite-difference solver for geophysical flows[J]. J. Comput. Phys., 1998,140:459-480.
    [108] Strang G, On the construction and comparison of difference schemes[J], SIAM J. Num. Anal, Vol.5, 506-517, 1968, 5:506-517.
    [109] Svendsen, LA. and P.A. Madsen, A Turbulent Bore on a Beach[J]. J. of Fluid Mechanics,1984, 148: 73-96.
    [110] Sykes, G.G., The Colorado Delta[M], American Geographic Society Special Publication 19, New York, 1937, 193 p., and Carnegie Institute, Washington, Publication 460, 193 p. 1945,A westerly trend: Tucson, Ariz., University of Arizona Press, 325 p.
    [111] Tamamidis P. and Assanis D. N., Evaluation of various high-order-accuracy schemes with and without flux limiters[J], Int. J. Numer. Methods in Fluids, 1993, 16: 931-948.
    [112] Tomas C R,Nieto F,Macarena G M.A flux-splitting solver for shallow water equations with source terms[J]. Int. J. Numer. Methods in Fluids. 2003,42:23-55.
    [113] Toro EF. Riemann problems and the WAF method for solving the two-dimensioanl shallow water equations[J]. Phil Trans R Soc, Lond A, 1992, 338: 43-67.
    [114] Toro EF. Riemann solvers and numerial methods for fluid dynamics[M]. Berlin: Springer,1999.
    [115] Toro EF. Shock-capturing methods for free-surface shallow flows[M]. Chichester: John Wiley & Sons, 2001.
    [116] Treske,A., Undular Bore in Channels-Experimental Studies[J], J. Hydraul. Res., 1994, 32(3):355-370.
    [117] Tricker, R.A.R., Bores, breakers, waves, and wakes~An introduction to the study of waves on water[M], New York, Elsevier, 1965, 250 p.
    [118] Tseng M H. Two-dimensional shallow water flows using TVD-MacCormack Scheme[J],Journal of Hydraulics Research., 2000, 38(2): 123-131.
    [119] Tseng M H. The improved surface gradient method for flows simulation in variable bed topography channel using TVD-MacCormack scheme[J], Int. J. Numer. Methods in Fluids, 2003, 43(1):71-91
    [120] Tull K A., Rulifson R A.,Striped Bass Spawning in a Tidal Bore River: The Shubenacadie Estuary, Atlantic Canada[J], Transactions of the American Fisheries Society, 1999, 128: 613-624
    [121] Uncles R.J., J.A. Stephens, D.J. Law, Turbidity maximum in the macrotidal, highly turbid Humber Estuary, UK: Flocs, fluid mud, stationary suspensions and tidal bores[J], Estuarine,Coastal and Shelf Science, 2006, 67: 30-52.
    [122] Van Leer, B. 1974, Towards the ultimate conservative difference scheme II: Monotonicity and conservation combined in a second order scheme[J]. J. Comput. Phys., 14, 361-370.
    [123] Vazquez M.E.,Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry[J]. J. Comput. Phys., 1999, 148:497-526.
    [124] Vincent S, Caltagirone J-P and Bonneton P, Numerical modeling of bore propagation and run-up on sloping using a MacCormack TVD scheme[J]. J. Hydraul. Res., 2001, 39(1):41-49.
    [125] Vukovic S, Sopta L, ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations[J], J. Comput. Phys., 2002, 179:593-621.
    [126] Whangpoo Conservancy Board, Report on hydrology of Hangchow Bay and the Chien-Tang Estuary[R], Printed by the North-China Daily News &Herald, LTD, 1921, Shanghai.
    [127] Waters, B., Severn tide[M], London, J.M. Dent and Sons, 1947,183p.
    [128] Whitham, G.B., Linear and nonlinear waves[M], Wiley New York, 1974.
    [129] Wolanskia E, Williamsb D, Spagnola S, Chanson H, Undular tidal bore dynamics in the Daly Estuary, Northern Australia[J], Estuarine, Coastal and Shelf Science, 2004, 60: 629-636.
    [130] Xing Yulong, Shu Chi-Wang, High order finite difference WENO schemes with the exact conservation property for the shallow water equations[J], J. Comput. Phys., 2005, 208: 206-227.
    [131] Xu Kun, Martinelli L, Jameson A. Gas-kinetic finite volume methods, flux-vector splitting and artificial diffusion[J]. J. Comput. Phys., 1995, 120: 48-65.
    [132] Xu Kun. Gas-kinetic scheme for unsteady compressible flow simulations[A], 29th Computational Fluid Dynamics, Von Karman Institute for Fluid Dynamics Lecture Series 1998-03, 1998.
    [133] Xu Kun. Unsplitting BGK-type schemes for the shallow water equations[J], International Journal of Modern Physics C, 1999, 10(4): 505-516.
    [134] Xu Kun. A gas-kinetic BGK scheme for the Navier-Stokes equations, and its connection with artificial dissipation and Godunov method[J], J. Comput. Phys., 2001a, 171: 289-335.
    [135] Xu Kun and Li ZW. Dissipative mechanism in G0dunov-type schemes[J], Int. J. Numer. Methods in Fluids, 2001b, 37: 1-22.
    [136] Xu Kun. A well-balanced gas-kinetic scheme for the shallow-water equations with source terms[J], J. Comput. Phys., 2002, 178: 533-562.
    [137] Xu Kun. Discontinuous Galerkin BGK method for viscous flow equations: one-dimensional system[J], SIAM J. Sci. Comput., 2004, 25(6): 1941-1963.
    [138] Yeh H. H. and Mok Kai-Meng, On turbulence in bores[J], Physics Fluid A, 1990, 2(5): 821-828
    [139] Zhang S Q, Ghidaoui M S, Gray W G, Li N Z. A kinetic flux vector splitting scheme for shallow water flows[J]. Advances in Water Resources, 2003, 26: 635—647.
    [140] Zhao DH, Shen HW, TabiosⅢ GQ et al. Finite-volume two-dimensional unsteady-flow model for river basins[J], J. of Hydraul. Eng., 1994, 120(7): 863-883.
    [141] Zhao D. H., Shen H. W., Lai J. S. and Tabios G. Q., Approximate riemann solvers in FVM for 2D hydraulic shock wave modeling[J], J. of Hydraul. Eng., 1996, 122(12): 692-702.
    [142] Zhou JG, Causon D M,. Mingham C Get al. The surface gradient method for the treatment of source terms in the shallow-water equations[J]. J. Comput. Phys., 2001, 168: 1-25.
    [143] Zienkiewicz O. C., Ortiz P., A split-characteristic based finite element model for the shallow water equations[J], Int. J. Numer. Methods in Fluids, 1995, 20 (8-9): 1061-1080.
    [144] 白玉川,许栋,王玉琦,张梅亭.二维溃坝波遇障碍物的水流泥沙数值模拟[J],水利学报,2005,36(5):538-543。
    [145] 鲍远林,周晓阳.移动边界的有限体积KFVS方法在一维溃坝波计算中的应用[J],水利学报,2005,36(12):1470-1475。
    [146] 陈希海.钱塘江涌潮动力浅析[J],河口与海岸工程,1993,(1-2):35~50。
    [147] 陈沈良,谷国传,刘勇胜.长江口北支涌潮的形成条件及其初生地探讨[J],水利学报,2003a,(11):30-36
    [148] 陈沈良,陈吉余,谷国传.长江口北支的涌潮及对河口的影响[J],华东师范大学学报(自然科学版),2003b,(2):74-80。
    [149] 程文辉,王船海.用正交曲线网格及“冻结”法计算河道流速场[J],水利学报,1988,(6):16-25。
    [150] 曹祖德,王桂芬.波浪掀沙、潮流输沙的数值模拟[J].海洋学报,1993,15(1):107-118。
    [151] 蔡启富,郑邦民.溃坝洪水波在天然梯级水库中的传播[J],水电能源科学,1997,15(4):12-16。
    [152] 邓家泉.以波尔兹曼方程建立明渠水流模型的理论基础[J],人民珠江,2000,(6):4-9。
    [153] 邓家泉.二维明渠非恒定水流BGK数值模型[J],水利学报,2002,(4):1-7。
    [154] 郭永涛,魏文礼.基于ENO格式的一维溃坝水流数值模拟[J],西安理工大学学报,2005,21(3):293-295。
    [155] 韩曾萃,戴泽蘅,李光炳主编.钱塘江河口治理开发[M],中国水利水电出版社,2003a。
    [156] 韩曾萃,史英标,周文波.大型调节水库对河口河床冲淤的影响[J],泥沙研究,2003b,(3):29-31。
    [157] 何少苓,王连祥.窄缝法在二维边界变动水域计算中的应用[J],水利学报,1986,(12):1l-19。
    [158] 胡四一,谭维炎.用TVD格式预测溃坝洪水波的演进[J],水利学报,1989,(7):1-11。
    [159] 胡四一,谭维炎.一维不恒定明流计算的兰种高性能差分格式[J],水科学进展.1991,2(1):11-21
    [160] 金旦华,刘国俊,周本华.一维涌潮计算[J],应用数学与计算数学,1965,3(2):183-195。
    [161] 吕江,祝梅良,翟洪刚.涌潮冲击丁坝的数值计算[J],海岸工程,2005a,24(1):1-8.
    [162] 吕江,朱陆明,翟洪刚.涌潮冲击丁坝时涌潮压力初步研究[J],科技通报,2005b,21(1):34-40
    [163] 李孟国.海岸河口泥沙数学模型研究进展[J],海洋工程,2006,24(1):139-154。
    [164] 李绍武,卢丽锋,时钟.河口准三维涌潮数学模型研究[J],水动力学研究与进展,A辑,2004,19(4):407-415。
    [165] 李约瑟编.中国科学史[M],科学出版社,1975。
    [166] 廖迎娣,张玮.基于自适应BP网络的涌潮波速计算模型[J],海洋工程,2003,21(4):70-74
    [167] 林斌炎.钱塘江下游水资源综合开发方案的设想[R],浙江省钱塘江管理局,2002。
    [168] 林炳尧.浅水流动中涌潮的形成[J],水动力学研究与进展,1988,3(4):63-69。
    [169] 林炳尧,周潮生,黄世昌.关于涌潮的研究[J],自然杂志,1998a,20(1):28-33。
    [170] 林炳尧,黄世昌,毛献忠.波状水跃和波状涌潮分析[J],水动力学研究与进展,1998b,13(1):106-115。
    [171] 林炳尧,黄世昌,周潮生.涌潮的反射和碰撞:回头潮和交叉潮[J],浙江水利水电专科学校学报,2000,12(1):6-10
    [172] 林炳尧,黄世昌,毛献忠,潘存鸿等.钱塘江河口潮波变化过程[J],水动力学研究与进展A辑,2002,17(6):665-675.
    [173] 林炳尧,黄世昌,潘存鸿.涌波的基本性质[J],长江科学院院报,2003,20(6):12-14。
    [174] 刘儒勋,舒其望.计算流体力学的若干新方法[M],科学出版社,2003。
    [175] 卢祥兴,杨火其,曾剑.钱塘江下游建桥对涌潮景观影响的研究[J],海洋学研究,2006,24(1):37-42。
    [176] 刘斌,方红卫,段杰辉.干湿边界的斜对角笛卡尔方法在平面二维水沙数学模型中的应用[J],泥沙研究,2006,(2):37-45。
    [177] 钱塘江志编纂委员会.钱塘江志[M],方志出版社,1998。
    [178] 毛献忠,潘存鸿.移动边界浅水问题的数值研究[J],水动力学研究与进展,2002,A辑,17(4):507-513。
    [179] 潘存鸿,鲁海燕,陈甫源,赵鑫.涌潮数学模型在钱塘江河口桥梁工程中的应用[J],浙江水利科技,2004,135(5):1-4。
    [180] 潘存鸿,鲁海燕,林炳尧等.钱塘江涌潮分析和计算[R],浙江省水利河口研究院科研报告,2005。
    [181] 潘存鸿,徐昆.三角形网格下求解二维浅水方程的KFVS格式[J],水利学报,2006,37(7):858-864。
    [182] 潘雨村,张怀新.用密度函数法对自由表面进行数值模拟,水动力学研究与进展,A辑,2004,19(6):726-732。
    [183] 彭凯,方铎,曹叔尤.在二维流动计算中应用“河床切削”技术处理动边界问题[J],水动力学研究与进展,1992,A辑,7(2):200-205。
    [184] 邵卫云,毛根海,刘国华.钱塘江涌潮压力的分析与研究[J],水动力学研究与进展,A辑,2002,17(5):604~610.
    [185] 沈阿四.钱塘江涌潮形成的历史探索[J],浙江水利科技,2002,(3):75-76。
    [186] 沈焕庭.长江河口悬沙输移特性[M],长江口动力过程及地貌演变,上海科学技术出版社,1988。
    [187] 史宏达,刘臻.溃坝水流数值模拟研究进展[J],水科学进展,2006,17(1):129-135。
    [188] 苏铭德,黄素逸.计算流体力学基础[M],清华大学出版社,1997。
    [189] 苏铭德,徐昕,朱锦林.数值模拟在钱塘江涌潮分析中的应用——Ⅰ数值计算方法[J],力学学报,1999a,31(5):521-533。
    [190] 苏铭德,徐昕,朱锦林.数值模拟在钱塘江涌潮分析中的应用——Ⅱ计算结果分析[J],力学学报,1999b,31(6):700-716。
    [191] 宋正海,郭永芳,陈瑞平编.中国古代海洋学史[M],海洋出版社,1986。
    [192] 杜勇.河口变形效应与涌潮的形成[J],青岛海洋大学学报,1989,19(3):28-33。
    [193] 杜勇.河口均匀流涌潮波的形式[J],海洋与湖沼,199l,22(1):78-83。
    [194] 杜珊珊,薛雷平.长江口北支涌潮的一维数值模拟[J],上海水务,2006,22(2):44-47。
    [195] 谭维炎,胡四一.二维浅水流动的一种普适的高性能格式(有限体积Osher格式)[J],水科学进展,1991,2(3):154-161
    [196] 谭维炎,胡四一.浅水流动计算中一阶有限体积法Osher格式的实现[J],水科学进展,1994,5(4):262-270。
    [197] 谭维炎,胡四一,韩曾萃等.钱塘江涌潮的二维数值模拟[J],水科学进展,1995,6(2):83-93。
    [198] 谭维炎.计算浅水动力学—有限体积法的应用[M],清华大学出版社,1998.
    [199] 万德成,缪国平.数值模拟波浪翻越直立方柱[J],水动力学研究与进展,A辑,1998,13(3):363-370。
    [200] 汪迎春.溃坝水流二维演进模型[D],河海大学硕士学位论文,2001。
    [201] 王嘉松,倪汉根,金生.二维溃坝波传播和绕流特性的高精度数值模拟[J],水利学报,1998,(10):1-6
    [202] 王立辉.渍坝水流数值模拟与溃坝风险分析研究[D],南京水利科学研究院博士学位论文,2006。
    [203] 王志刚,汪德爟,赖锡军,周杰,陈扬.下游为干河床的溃坝水流数值模拟[J],水利水运工程学报,2003,(2):18-23。
    [204] 王如云.浅水波方程的TVD有限差分数值模拟[J].海洋与湖沼,1991,22(2):115-123。
    [205] 王如云.浅水涌波数值模拟的Roe平均法[J],计算物理,2000,17(1-2):199-203。
    [206] 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):1-9。
    [207] 蔚喜军,周铁.流体力学方程的间断有限元方法[J],计算物理,2005,22(2):108-116。
    [208] 魏文礼.金忠青.复杂边界河道流速场的数值模拟[J],水利学报,1994,(11):26-30。
    [209] 吴维庆.涌潮形成条件及计算[R],南京水利科学研究所研究报告汇编(河港研究第二分册),1963。
    [210] 严恺.海岸工程[M],海洋出版社,2002年,P10。
    [211] 杨国丽,魏文礼,郭永涛.基于WENO格式的一维渍坝波的数值计算[J],西安理工大学学报,2006,22(4):435-437。
    [212] 杨火其,吴一鸣,林炳尧.强潮河口护塘丁坝上游冲刷研究[J],水道港口,2000,21(1):14-18。
    [213] 杨火其,王文杰.钱塘江河口导型块体抗冲稳定特性试验研究[J],长江科学院院报,2001,4:19-22。
    [214] 杨继明.对流占优对流扩散方程的间断有限元(DG)解法[J],湖南工程学院学报(自然科学版),2006,16(1):67-69。
    [215] 于普兵.二维浅水水流数值模拟技术研究——无结构网格有限体积法[D],南京水利科学研究硕士学位论文,2006。
    [216] 曾剑.钱塘江河口建桥对涌潮的影响分析[D],浙江大学硕士学位论文,2004。
    [217] 曾剑,熊绍隆,潘存鸿,林炳尧.运用神经网络理论研究钱塘江涌潮的影响因素[J],长江科学院院报,2006,23(5):14-16
    [218] 张增产,沈孟育.改进的时空守恒元和解元方法[J],清华大学学报,1997a,(8):65-68.
    [219] 张增产,沈孟育.一种严格保证时-空守恒率的数值方法[J],计算物理,1997b,14(6):835-841.
    [220] 张增产,沈孟育.用时空守恒方法求带源项及刚性源项的守恒率方程[J],清华大学学报,1998,(11):87-90.
    [221] 张增产,沈孟育.求解二维Euler方程的时.空守恒格式[J],力学学报,1999,(2):1-7.
    [222] 张永祥,陈景秋,韦春霞.一维溃坝洪水波的数值模拟-时空守恒法[J],重庆大学学报,2005a,28(5):136-139。
    [223] 张永祥,陈景秋.用守恒元和解元法数值模拟二维溃坝洪水波[J],水利学报,2005b,36(10):1-8
    [224] 张玮,徐金环,李国臣,吴维钧.涌潮分析与波速计算[J],水利水运科学研究,1999,(2):158-164
    [225] 张书农.治河工程学[M],上海:中国科学图书仪器公司,1951。
    [226] 赵棣华,谭仁忠,谭维炎.长江口南支河段悬移质含沙量计算模型[J],泥沙研究,1990,(2):54-62。
    [227] 赵雪华.钱塘江涌潮的一维数学模型[J],水利学报,1985,(1):50~54。
    [228] 赵渭军,韩海骞,林炳尧.涌潮水流条件下排桩式低丁坝水力学冲淤试验研究[J],水动力学研究与进展,2001,16(3):62-69。
    [229] 周胜,杨永楚.钱塘江水下防护工程研究与实践[J],水利学报,1992,(1):20-30。
    [230] 朱军政,林炳尧.涌潮翻越丁坝过程数值试验初步研究[J],水动力学研究与进展,2003,A辑,18(6):671-678。
    [231] 朱德军,陈永灿,刘昭伟.处理二维浅水流动中动边界问题的淹没节点法[J],水动力学研究与进展,A辑,2006,21(1):102-106。
    [232] 钟德钰,彭杨,张红武.多沙河流的非恒定一维水沙数学模型及其应用[J],水科学进展,2004,15(6):706-710。

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700