| 曲线坐标系下三维水动力模型求解新方法 |
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| 引用本文： | 吴卫国,;沈露予,;薛世峰.曲线坐标系下三维水动力模型求解新方法[J].排灌机械,2014(4):333-342. |
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| 作者姓名： | 吴卫国 ;沈露予 ;薛世峰 |
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| 作者单位： | [1]中国石油大学华东储运与建筑工程学院,山东青岛266555; [2]南京信息工程大学海洋科学学院,江苏南京210044 |
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| 基金项目： | 国家自然科学基金资助项目（11172143）; 江苏省普通高校研究生科研创新计划资助项目（CXZZ13_0518） |
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| 摘 要： | 为求解三维水动力模型的高精度数值计算,设计了一种在曲线坐标系下求解的新方法.对ξ,η和ζ共3个方向的空间导数分别采用高精度的紧致有限差分以及非线性项的迎风紧致有限差分格式,时间积分则采用四阶修正Runge-Kutta显式格式.为了验证该算法求解曲线坐标系下三维水动力模型的正确性,选取与De Vriend的180°弯道水槽试验相同的物理参数进行数值试验,计算出水位、流速分布等,并将计算结果与De Vriend的试验值以及先前采用SIMPLEC法获得的数值结果进行了对比分析.结果发现：文中创建的高精度算法获得的数值解比SIMPLEC法计算的数值结果更符合试验值,通过算法定量计算得到的平均速度值与试验测量值之间产生的最大相对误差约为3%.说明构建的高精度紧致有限差分算法来数值求解三维水动力问题是可行的、合理的,为天然河道、明渠以及湖泊等水动力计算提供参考依据.
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| 关 键 词： | 紧致有限差分 水动力模型 曲线坐标 Runge-Kutta格式 |
New method of investigation on 3D hydrodynamic model in curvilinear coordinates |
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| Institution: | Wu Weiguo, Shen Luyu, Xue Shifeng ( 1. College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao, Shandong 266555, China; 2. School of Marine Science, Nanjing University of Information Science ＆ Technology, Nanjing, Jiangsu 210044, China) |
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| Abstract: | A numerical method for solving three-dimensional hydrodynamic model in curvilinear coordinates was presented. High-order and high-resolution compact finite difference scheme and upwind compact finite difference scheme for nonlinear terms were used as spatial discretization, and the time integration was accomplished by 4th-order modified Runge - Kutta scheme. To verify the numerical method, the same physical parameters of De Vriend＇s 180° curved channel test were used in the simulation. The results show that, the new numerical results are closer to the experimental data than the results calculated by using SIMPLEC. The maximum relative error between numerical and experimental average velocity results is less than 3%. It is proved that the numerical method presented is feasible and rational. To sum up, it is an efficient, feasible and rational way to numerically solve hydrodynamic problems, and can be used in many engineering computations of territorial waters as natural rivers, open channels and lakes with arbitrary complex boundaries. |
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| Keywords: | compact finite difference schemes 3D hydrodynamic model curvilinear coordinates Runge - Kutta scheme |
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