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排灌机械工程学报
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排灌机械工程学报  0, Vol. Issue (): 20-    DOI:
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任意曲线坐标系下二维浅水方程的数值模拟
吴卫国
Numerical Simulation of 2D Shallow Water Equation in  Arbitrary Curvilinear Coordinates
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摘要 在自然界中,河流、长江、湖泊、港口河口以及海湾水环境质量恶化的现象已成为我国一个突出的环境问题。在综合治理水污染环境时,必需掌握水动力及水质的运动、迁移规律,才能进行预测及治理。因此,建立任意曲线坐标系下的水动力模型是相当重要的。本文采用拟合边界曲线的方法来模拟天然河道的复杂边界问题,将模拟后的任意二维浅水方程和 方程封闭联立求解。求解的数值方法,采用ADI差分格;以De Vriend的1800平面弯道水槽实验模型为例,数值计算任意曲线坐标系下二维浅水方程的数值解;将本文数值模拟的结果和De Vriend的实验结果进行验证,其结果是相当令人满意的,这证明了本文采用的数值方法是可靠的、正确的,也将为任意复杂边界的天然河道水动力计算提供合理可行的计算手段。
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关键词曲线坐标   浅水方程   方程   ADI差分格式   数值模拟     
Abstract: In nature, the water quality deterioration phenomenon of river, the Yangtze River, lakes, estuaries and port bay has become a highlight problem of water environment to our country. In the comprehensive management of water pollution of the environment, the hydrodynamic and water quality of movement, migration need to be mastered to predict and control the pollution. Therefore, it is quite important to establishment the hydrodynamic mode in arbitrary curve coordinate. This paper uses the boundary curve fitting method to simulate the natural river channel for the complex boundary, and to simulate the shallow water equations and the   equations which are closed and linked simultaneously. A numerical method, ADI difference scheme, is used to discrete the equations, numerical calculating 2D shallow water equations in curvilinear coordinates. Take the De Vriend’s 1800 plane curve flume experiment model as example, the numerical simulation results in this paper is validated with the experimental results of De Vriend, which is quite satisfactory. This proves that the numerical method established in this paper are reliable and correct, and it will provide reasonable and feasible means of calculation for Natural River hydrodynamic with arbitrarily complex boundary.
Key wordsCurvilinear coordinates, Shallow water equation,    equation, ADI difference scheme, Numerical simulation   
引用本文:   
. 任意曲线坐标系下二维浅水方程的数值模拟[J]. 排灌机械工程学报, 0, (): 20-.
. Numerical Simulation of 2D Shallow Water Equation in  Arbitrary Curvilinear Coordinates[J]. Journal of Drainage and Irrigation Machinery Engin, 0, (): 20-.
 
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