河道与渐溃堤坝耦联的水力数值模拟的研究
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摘要
河堤溃决后的溃堤波会对圩区造成很大的危害，对溃堤波的研究是一个重要课题，研究其演进过程具有重要意义。本文将河道与堤坝下游区域视为一个整体，对于单一河道采用Preissmann四点隐式差分格式计算，对于溃口及圩区采用有限体积法，建立了一维河道与堤坝渐溃耦联的水力模型，也是一维、二维耦合的水流模型。在应用有限体积法无结构网格的基础上建立了高性能的TVD—MUSCL格式，根据堤坝溃口处的流量、水位，计算出沿程下游各点的流速、水位。算例验证表明：应用组合型TVD—MUSCL格式配合有限体积法是一种高解析度的数值方法，且TVD—MUSCL格式对于自动捕捉激波和抑制间断附近的数值解波动十分有效，它对间断具有高分辨率。本文建立逐渐溃堤的水力模型首次对二维逐渐溃堤波的流动问题进行了数值研究，揭示了逐渐溃堤过程中溃口处流场的变化情况，以及溃堤波的传播、绕射、反射及变形的复杂运动特征，能较好地模拟实际工程中的溃堤失事，模拟比较逼近于真实溃决过程，计算精度可满足工程要求。其研究成果能够为防汛部门的正确决策以及溃堤灾害性分析和防灾减灾提供科学的依据，具有较大的实际指导意义。
The dike-break long waves cause great damage to polder, and then it is a significant subject for studying the dike-break long wave. It is significant of research for the propagating of the dike-break wave. In the paper, river and the downstream area of dike are regarded as a whole system, and hydraulic model of coupling 1-D river and gradual dike-break is established, therein the Preissmann implicit difference scheme is applied to Main River, and the FVM (Finite Volume Method) is applied to the breach and polder. On the basis of FVM and unstructured grids, TVD ?MUSCL scheme is constructed with high performance. According to the discharge and water level of breach, the scheme is used to compute velocity and water level of center node of all elements. The results show that it is the numerical method of high analyzable degree for the hybrid TVD scheme combinated with FVM, and the scheme is not only sufficiently accurate and nonoscillatory, but also capable of treating automatically hydraulic jump. The hydrauli
c model of gradual dike-break simulates numerically the 2-D flow of gradual dike-break waves. It shows the variation of flow field on breach, and the complicated flow characteristic of the propagation, diffraction, reflection and deformation of the dike-break waves. The hydraulic model can realistically simulate the burst process of dike, and computational accuracy is satisfied with the engineering demands. It is concluded that the model and methods have scientific decision reference and practical significance for flood warning service, and provide scientific basis for the analysis and prevention of disaster caused by dike destruction.
The dike-break long waves cause great damage to polder, and then it is a significant subject for studying the dike-break long wave. It is significant of research for the propagating of the dike-break wave. In the paper, river and the downstream area of dike are regarded as a whole system, and hydraulic model of coupling 1-D river and gradual dike-break is established, therein the Preissmann implicit difference scheme is applied to Main River, and the FVM (Finite Volume Method) is applied to the breach and polder. On the basis of FVM and unstructured grids, TVD ?MUSCL scheme is constructed with high performance. According to the discharge and water level of breach, the scheme is used to compute velocity and water level of center node of all elements. The results show that it is the numerical method of high analyzable degree for the hybrid TVD scheme combinated with FVM, and the scheme is not only sufficiently accurate and nonoscillatory, but also capable of treating automatically hydraulic jump. The hydrauli
c model of gradual dike-break simulates numerically the 2-D flow of gradual dike-break waves. It shows the variation of flow field on breach, and the complicated flow characteristic of the propagation, diffraction, reflection and deformation of the dike-break waves. The hydraulic model can realistically simulate the burst process of dike, and computational accuracy is satisfied with the engineering demands. It is concluded that the model and methods have scientific decision reference and practical significance for flood warning service, and provide scientific basis for the analysis and prevention of disaster caused by dike destruction.
引文
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[30] 傅德薰 熵条件及差分方程的数值解 第二届全国计算流体力学方法会议论文集，1983
[31] 傅光明 傅德薰 超音速绕流计算中熵条件的几个问题 第一届全国计算流体力学方法会议论文集，1981
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[33] Steger J and Warming R F. Flux vector splitting of the inviscid gas-dynamics equations with application to finite methods. NASA TMD-78605, 1979
[34] 傅德薰 马延文 气动计算中一个简单有效的差分格式 空气动力学学报，1985(2)
[35] 马延文 傅德薰 数值计算可压缩Navier-Stokes方程的一个新的系数矩阵分裂法 计算物理，1985(2)
[36] Garten A. On a class of high resolution total-variation-stable finite-difference schemes. NYU Report, Oct.1982
[37] Roe P L. Some contributions to the modeling of discontinuous flows. AMS-SIAM Seminar, Sam Diego, June 1983
[38] Var Leer B. Towards the ultimate conservative difference scheme. Journal of Computational Physics.1974(14): 363～389
[39] Osher S. Shock modeling in transonic and supersonic flow recent advances in numerical methods in fluids. Vol.4, W.G.Habashi Ed
[40] Yee H C, Warming R F and Harten A. Implicit total variation diminishing (TVD) schemes for steady-state calculations. AIAA Paper 83-1902, 1983
[41] Harten A and Hyman J M. A self-adjusting grid for the computation of weak solutions of hyperbolic conservation laws. Los Alamos Nat. Lab. Report LA. 9105, 1981
[42] Yee H C. Construction of explicit and implicit symmetric TVD schemes and their applications. Journal of Comp. Phys., 1987(68): 151～179
[43] Harten A. On high-order accurate interpolation for non-oscillatory shock-capturing schemes. The IMA Volumes in Mathematics and its Applications .Springer-Verlag 1986 (2): 71～106
[44] 谭维炎 浅水动力学的回顾和当代前言问题水科学进展 Vol．18，No．2 Mar．，2001：97～105
[45] Desiseri D and Jameson A. Multigrid solution of the Euler equations on unstructured and adaptive meshes. AIAA Paper 87-0353, 1987
[46] Pan D and Cheng J. Incompressible flow solution on unstructured triangular meshes. Int. J. Numer. Methods Fluids. 19939(16): 1079～1098
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