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清华大学学报(自然科学版)  2015, Vol. 55 Issue (7): 797-802    
  热能工程 本期目录 | 过刊浏览 | 高级检索 |
求解势流的正则化快速多极子边界元法
翟杰, 祝宝山, 曹树良
清华大学 热能工程系, 水沙科学与水利水电工程国家重点实验室, 北京 100084
Regularization fast multipole boundary element method for solving potential flow problems
ZHAI Jie, ZHU Baoshan, CAO Shuliang
State Key Laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
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摘要 该文将快速多极子算法和处理强奇异积分的正则化算法应用于传统边界元法中, 开发了正则化快速多极子边界元法。该方法既可以解决传统边界元法计算量和存储量会随着单元数量的增加而快速增加的问题, 也可以处理边界元法求解势流速度和速度梯度时产生的强奇异性积分问题。将所开发的方法应用于绕球势流的数值计算中, 计算结果证明了方法的可靠性和高效性; 对相关计算参数影响的分析为复杂边界流动问题的计算提供了参考依据。
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翟杰
祝宝山
曹树良
关键词 势流问题边界元法快速多极子法正则化算法    
Abstract:The fast multipole method and the regularization algorithm are combined to process the strong singular integral in the conventional boundary element method for potential flow problems. This method reduces the number of calculations and the storage which increases sharply with the number of elements in the conventional boundary element method. This method can also handle strongly singular integrals for calculating the velocities and the velocity gradient for potential flow by directly differentiating the boundary integral equation. The method is applied to simulate potential flow over a sphere. The results show that this method is accurate and efficient. This model is used to analyze the influence of the calculation parameters for other complicated boundary condition problems.
Key wordspotential problem    boundary element method (BEM)    fast multipole method (FMM)    regularization algorithm
收稿日期: 2014-12-16      出版日期: 2015-07-15
ZTFLH:  O351.3  
通讯作者: 祝宝山,副教授,E-mail:bszhu@mail.tsinghua.edu.cn     E-mail: bszhu@mail.tsinghua.edu.cn
引用本文:   
翟杰, 祝宝山, 曹树良. 求解势流的正则化快速多极子边界元法[J]. 清华大学学报(自然科学版), 2015, 55(7): 797-802.
ZHAI Jie, ZHU Baoshan, CAO Shuliang. Regularization fast multipole boundary element method for solving potential flow problems. Journal of Tsinghua University(Science and Technology), 2015, 55(7): 797-802.
链接本文:  
http://jst.tsinghuajournals.com/CN/  或          http://jst.tsinghuajournals.com/CN/Y2015/V55/I7/797
  图1 三角形等参元示意图
  图2 数学模型示意图
  图3 球边界单元划分
  图4 φ=0平面内球表面速度势函数分布
  表1 单球绕流问题计算精度比较
  图5 BEM 和rFMBEM 计算时间比较
  图6 多极子开展级数p 的影响
  图7 最大节点数s的影响
  图8 φ=0平面内多球绕流的速度分布图
  图9 BEM 和rFMBEM 计算多球绕流的数值结果比较
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