摘要
明渠水流运动在实际工程中广泛存在，其数值模拟研究有现实意
义。桥墩壅水是在防洪标准低、防洪费用高的平原河道上修建桥梁时必
须重点考虑的问题之一，其研究具有重要价值。
本论文采用非规则贴体网格有限体积法和显式MacCormack预测-
校正法求解平面二维水深积分方程，对明渠水流运动的数值模拟方法进
行了研究，并且应用该数值模型计算了14种不同的桥墩体型、来流、收
缩比的组合工况下的桥墩壅水问题。采用模型试验资料验证了壅水高度
计算结果。
非规则贴体网格有限体积法可以真实模拟复杂形状边界，提高边界
附近的计算精度，能够较其他方法更理想地处理明渠水流中常常遇到的
复杂边界问题，在这点上比只能构造少的单元数的有限单元法和一般采
用矩形网格的有限差分法优越。
壅水高度的计算结果与模型试验资料吻合较好，证明了数值模型是
可靠的。
此外，本论文还初步研究了网格局部加密方法并应用于桥墩局部绕
流流场的研究。网格局部加密方法的应用明显的改善了加密区域内的结
果，对加密区域外的流场也有一定的改进，具有一定的应用前景。
Open channel flow exists widely and its numerical simulation is of reality. The damming caused by a bridge pier is one of the aspects considered intentionly while building a bridge on a river which flood control standard is low and flood control cost is high so the study of damming is of important value.
In this thesis a numerical model to solve the planear 2-D Depth-Integrated Flow(DIF) has been established with irregular body-fitted mesh Finite Volume Method and explicit MacCormack predictor-corrector method and applied to the study of damming caused by a bridge pier under 14 working conditions varied with the combination of different pier shape . flow rate and contraction ratio. The experimental results in a physical model are adopted to verify the simulated damming heights.
Irregular body-fitted mesh Finite Volume Method can really simulate complicated boundaries and improve the predicting precision so it is more ideal to process the complicated boundaries met often in open channels. In this point of view this approach is better than Finete Element Method in which only few elements can be used and Finite Diffence Method in which the rectangular grid is always used.
That the predicted values of damming height agree well with the exprimental results proves the validity of the numerical model.
In the addition, the locally refining mesh method has been studied preliminarily and applied to the study of the local flow around a bridge pier. It is found that the use of the locally refining mesh method can improve the results in the refined area greatly, and can improve the results outside the refined area to a certain extent too. This method has the potential application in studying many problems with the great characteristic size ratio .
引文
(1) 张凌武，骆介华，妹滩枢纽坝区流场数学模型计算报告，研究报告，华东 勘测设计研究院，1991年10月．
(2) Wang, S.S.Y. and Jia, Y., Computational Modeling and Hydroscience Research, presented at Advances in Hydro-Science and-Engineering, Vol.2, March 22-26, 1995, Beijing, China, pp2147-2157．
(3) 周建军，林秉南，王连祥，河道平面二维水流数值计算，水利学报，第五期， 1991年5月，pp8-18．
(4) Han, G. and al., A Numerical Model for 3-D Flow in Open Channels, Journal of Hydrodynamics, Ser.B, Vol.4, No.1, 1992, pp1-7．
(5) 苑明顺，计算流体力学讲义，清华大学水利水电工程系，1994年2月．
(6) Chen, X. and Wang, X., Mathematical Modeling of Erosion in Flood Plain of the ChengXiHu Lake Sluice, presented at Advances in Hydro-Science and-Engineering, Vol.2, March 22-26, 1995, Beijing, China, pp2267-2274．
(7) 许建林，曹叔尤，方铎，吴持恭，河道平面二维流场和床面冲淤有限元数 值计算，’93全国水动力学研讨会文集，pp344-351．
(8) 程文辉，王航海，用正交曲线网格及“冻结”法计算河道流速场，水利学报， 第6期，1988年6月，pp18-25．
(9) 王航海，程文辉，河道二维非恒定流场计算方法研究，水利学报，第1期， 1991年1月，PP10-18．
(10) Stelling, G.S., On the Construction of Computational Methods for Shallow Water Flow Problems, Ph.D. Thesis, Delft Univ. of Technology, the Netherlands, 1983．
(11) Zhang, L., Numerical Solution of St. Venant Equation with a Generalized ADI Method, Research Report, East-China Hydroelectric Power Investigation and Design Institute, China.
(12) Stelling, G.S. and Wang, L.-X., Experiments and Computations on Unsteady Seperating Flow in an Expanding Flume, Research Report, Delft Univ. of Technology, the Netherlands, 1984．
(13) 周雪漪，计算水力学，清华大学出版社，第一版，1995年9月，pp362-364．
(14) 董耀华，黄煜龄，河口潮汐河段二维非恒定流数模研究及应用，长江科学 院院报，1995年1月，PP10-19．
(15) 苑明顺，余子牛，CSSRC循环水槽内流道数值模拟(共三册)，研究报告， 中国管理科学研究院应用基础与工程科学研究所、清华大学，1995年4 月．
(16) 苑明顺，孙春柳，小湾电站泄水中孔研究数学模型体型优化设计阶段报告， 研究报告，清华大学水利水电工程系，1994年3月
(17) 苑明顺，陈长植，小湾电站泄水中孔体型优化设计与数学模型研究，研究 报告，清华大学水利水电工程系，1995年6月．
(18) Ven Te Chow, Open channel Hydraulics, 1959．
(19) 陈立业，沈曼莲，桥墩壅水问题的试验研究，研究报告，淮河水利委员会， 1986年11月．
(20) Lemos, F.O., Non-Steady Morphological Phenomena; Physical and Mathematical Modeling of Degradation (Including Local Scour) and Aggradation, General Report in Proceedings of 16th Congress of IAHR, Sao Paulo, Brasil, 27 July-1 August 1975．
(21) Ikeda, H., Three-Dimensional Flows around Bluff Bodies, Journal of Hydroscience and Hydraulic Engineering, No.s1-1 Hydraulics, Special Issues/1993 (JSCE), pp164-179．
(22) Vittal, N., Kothyari, V.C. and Haghighat, M., Clear-Water Scour around Bridge Pier Groups, Journal of Hydraulic Engineering (ASCE), Vol.120, No.11, Nov.1994, pp1309-1318．
(23) Melih, A., Study of Time-Dependent Local Scour around Bridge Piers, Journal of Hydraulic Engineering(ASCE), Vol.117, No.10, Oct.1991, pp1247-1268．
(24) 汪德(？)，计算水力学理论与应用，河海大学出版社，1989年1月，PP14-20．
(25) Lilly, D.K., On the Application of the Eddy Viscosity Concept in the Inertial Subrange of Turbulence, NCAR Manuscr.123, 1966．
(26) Deardorff, J.W., A Numerical Study of Three-Dimensional Channel Flow at Large Reynolds Numbers, J. Fluid Mech., Vol.41, Part 2．1970, pp453-480．
(27) Deardorff, J.W., On the Magnitude of the Subgrid Scale Eddy Coefficient, J. Comp. Phys,, Vol.7, 1971, pp120-133．
(28) Kwak, D., Reynolds, W.C. and Ferziger, J.H., Three-Dimensional Time-Dependent Computation of Turbulent Flow, Report TF-5, Dept. of Mcch. Eng., Stanford Univ., USA, 1975．
(29) Smagorinsky, J., Manabe, S. and Holloway, J.L., Numerical Results from a Nine Level General Circulation Model of the Atmosphere, Mon. Weath. Rev., Vol.93, No.12, 1965, pp727-768．
(30) Yuan, M., Weakly Compressible Flow Model and Simulations of Vortex-Shedding Flows about a Circular Cylinder, Ph.D. Thesis, Univ. of Minnesota, USA, 1988, pp10-19．
(31) 苑亚珍，船闸输水反弧门廊道非恒定流研究，硕士论文，清华大学水利水 电工程系，1994年3月．
(32) 苑明顺，高水头船闸输水系统急变分离流模拟分析，研究报告和’93全国 水动力学研讨会论文，清华大学水利水电工程系，1993年4月．
(33) 苑明顺，余子牛，三峡船闸输水闸门后廊道水流的数值模拟研究，研究报 告，清华大学水利水电工程系，1995年10月．
(34) Song, C.C.S. and Yuan., M., Simulation of Vortex-Shedding Flows about a Circular Cylinder at High Reynolds Number, J. Fluids Eng.(ASME), Vol.112, Jun.1990, pp155-161．
(35) Pegret, R. and Taylor, T.D., Computational Methods for Fluid Flow, Springer-Verlag, 10th version, 1982．
(36) Yuan, M., Song, C.C.S., He, J., Numerical Analysis of Turbulent Flow in a Two-Dimensional Non-Symmetric Plane-Wall Diffuser, J Fluids Eng.(ASME), Vol.113, Jun.1991, pp210-215．
(37) Yuan, M., Two-Dimensional Simulation of Flows in Plane-Wall Diffusers, J. of Hydrodynamics, Ser.B, Vol.4, No.4, 1992, pp43-53．
(38) Bobko, G., Numerical Solution of the Euler Equations for Almost Incompressible Flows, M.S. Thesis, Univ. of Minnesota, USA, 1985．
