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有限区域求解流函数和速度势的迭代调整方法及其收敛性分析

黎爱兵,  张立凤,  臧增亮,  张云

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文章导航 > 应用数学和力学  > 2012 >  33(6): 651-662
黎爱兵, 张立凤, 臧增亮, 张云. 有限区域求解流函数和速度势的迭代调整方法及其收敛性分析[J]. 应用数学和力学, 2012, 33(6): 651-662. doi: 10.3879/j.issn.1000-0887.2012.06.002
引用本文: 黎爱兵, 张立凤, 臧增亮, 张云. 有限区域求解流函数和速度势的迭代调整方法及其收敛性分析[J]. 应用数学和力学, 2012, 33(6): 651-662. doi: 10.3879/j.issn.1000-0887.2012.06.002
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LI Ai-bing, ZHANG Li-feng, ZANG Zeng-liang, ZHANG Yun. Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis[J]. Applied Mathematics and Mechanics, 2012, 33(6): 651-662. doi: 10.3879/j.issn.1000-0887.2012.06.002
Citation: LI Ai-bing, ZHANG Li-feng, ZANG Zeng-liang, ZHANG Yun. Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis[J]. Applied Mathematics and Mechanics, 2012, 33(6): 651-662. doi: 10.3879/j.issn.1000-0887.2012.06.002
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有限区域求解流函数和速度势的迭代调整方法及其收敛性分析

doi: 10.3879/j.issn.1000-0887.2012.06.002

  • 解放军理工大学 气象学院,南京 211101

基金项目: 国家自然科学基金资助项目(40975031)
详细信息
    通讯作者:

    黎爱兵(1985—),男,湖南益阳人,博士生(Tel:+86-25-80831403; E-mail:jeibing@126.com);张立凤(1961—),女,河北唐山人,教授(联系人.Tel:+86-25-80831403;E-mail:zhanglif@yeah.net).

  • 中图分类号: O302; P425

Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis

  • Institute of Meteorology, PLA University of Science and Technology,Nanjing 211101, P.R.China

    摘要
  • 摘要: 全球区域求解流函数和速度势的解是唯一的，但有限区域内，由于受区域边界条件限制，流函数和速度势的计算以及风场的分解不是唯一的，减小或消除边界不确定对结果的影响是有限区域求解流函数和速度势以及分解风场最重要的问题．该文在Endlich迭代调整思想上，提出了能准确求解有限区域流函数和速度势且对边界条件要求较低的迭代调整方法．该方法也能准确地分解和重建风场，且风场重建的误差非常小．对该迭代方法的收敛性进行分析，发现其收敛性与不同方向网格的格距和调整系数有关．最后将该方法应用到Arakawa A-D网格和不规则区域，验证了该方法的可靠性．
    Abstract: Stream function and velocity potential can be easily computed by solving Poisson equations in a unique way for the global domain. Because of various assumptions for handling boundary conditions, the solution is not unique when a limited domain is concerned. So, it is very important to reduce or eliminate the effects caused by uncertain boundary condition. An iterative and adjusting method based on the Endlich iteration method was presented to compute stream function and velocity potential for limited domains. This method did not need an explicitly specifying the boundary condition, while it could obtain the effective solution and was proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depended on relative value between the distances of grid in two different directions and was related to the value of the adjusting factor. Applying the method in Arakawa grids and irregular domains, the results showed that it could not only obtain accurate vorticity and divergence, but also accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method was accurate and reliable.
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出版历程
  • 收稿日期:  2011-09-26
  • 修回日期:  2012-03-01
  • 刊出日期:  2012-06-15

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