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A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING SHALLOW WATER EQUATIONS [4]

论文作者:Wang Jia-s 论文属性:短文 essay登出时间:2007-08-06编辑:点击率:11524

论文字数:18530论文编号:org200708061142142607语种:英语 English地区:中国价格:免费论文

关键词:HIGH RESOLUTION FINITE VOLUME METHODSHALLOW WATER EQUATIONS

The water depth inside the dam is 10m, whilst outside the dam is 1m. At the instant of dam failure the circular wall is assumed to be removed completely and no slope and friction is considered, then the circular dam-break waves will spread and propagate radially and symmetrically. The results with above method at time t=0.69s are shown in Figures 4 (a), (b) and (c) which denote the water surface elevation, contour of surface elevation and velocity field respectively. It can be clearly seen that the waves spread uniformly and symmetrically. These results agree quite well with those given by Alcrudo and Garcia-Navarro , Zhao et al. , Alastansiou and Chan and they can be tested each other. It demonstrates that the present method is reliable and fine. Fig. 3(c) Velocity field for a rectangular dam-break Fig. 4(a) Water surface elevation for a circular dam-break circular dam-break Fig. 4(b) Contour of surface elevation for a circular dam-break Fig. 4(c) Velocity field for a circular dam-break   7. SUMMARY AND CONCLUSIONS TVD scheme is playing an important role in gas dynamics because of its high accuracy, good shock-capturing ability and nonoscillatory numerical performance. But it is constructed based on finite difference method. In this paper a new geometry and topology is defined for the extension of nodes to elements. With the conservative type of the shallow water equations, a hybrid type second order TVD scheme is applied and two-step Runge –Kutta method is adopted in time, then a finite volume TVD scheme for the shallow water equations on arbitrary quadrilateral elements is developed. The numerical results of two types of dam-break problem show that the method is sufficiently robust and can handle discontinuities and complex flow problems efficiently. The results presented in this paper are in excellent agree with those reported recently and even display sharper discontinuities and the maximum values attenuate more slowly. It can be foreseen that this method has much broader application foreground. As for further studies, such as in the cases of a channel having bend, bifurcation and inner islands, will discuss in another paper. REFERENCES 1. A. Harten, 1983: High Resolution Schemes for Hyperbolic Conservation Laws, Journal of Computational Physics, 49, 357-393. 2. S. Y. Hu, W. Y. Tan, 1990: Numerical Modeling of Bores due to Dam-Break, Journal of Hydrodynamics, Ser. A., 5(2), 90~98 (in Chinese). 3. J. H. Tao, W. D. Zhang, 1993: The Simulation of One and Two Dimensional Dam-Breaking Waves by TVNI Scheme, Journal of Tian Jin University, (1), 7~15 (in Chinese). 4. J. Y. Yang, C. A. Hsu, and S. H. Chang, 1993: Computations of Free Surface Flows, Part 1: 1-D Dam-Break Flow, Journal of Hydraulic Research, 31(1). 5. J. S. Wang, H. G. Ni, S. Jin and J. C. Li, 1998: Simulation of 1D Dam-Break Flood Wave Routing and Reflection by Using TVD Schemes, Journal of Hydraulic Engineering, (5), 7~11 (in Chinese). 6. J. S. Wang, H. G. Ni, and S. Jin, 1998: A High Accurate Numerical Simulation of the Propagation and Diffraction for 2D Dam-Break Bores, Journal of Hydraulic Engineering, (10), 1~6 (in Chinese). 7. F. Alcrudo, P. Garcia-Navarro, 1993: A High Resolution Godunov-Type Scheme in Finite Volumes for the 2D Shallow Water Equation, International Journal for Numerical Method in Fluids, 16, 489-505 1993. 8. D. H. Zha论文英语论文网提供整理,提供论文代写英语论文代写代写论文代写英语论文代写留学生论文代写英文论文留学生论文代写相关核心关键词搜索。
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