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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

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
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

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
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

  • 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.
  • [1] Hawkins H F, Rosenthal S L. On the computation of stream function from the wind field[J]. Mon Wea Rev, 1965, 93(4):245-252.
    [2] 吕美仲, 候志明, 周毅. 动力气象学[M]. 北京:气象出版社, 2004:113-114. (L Mei-zhong, HOU Zhi-ming, ZHOU Yi. Dynamic Meteorology[M]. Beijing: Meteorological Press, 2004:113-114.(in Chinese))
    [3] Frederiksen J S, Frederiksen C S. Monsoon disturbances, intraseasonal oscillations, teleconnection patterns, blocking, and storm tracks of the global atmosphere during January 1979: linear theory[J]. J Atmos Sci, 1993, 50(10):1349-1372.
    [4] Knutson T R, Weickmann K M. 30~60 day atmospheric oscillations: composite life cycles of convection and circulation anomalies[J]. Mon Wea Rev, 1987, 115(7):1407-1436.
    [5] Lorenc A C, Ballard S P, Bell R S, Ingleby N B, Andrews P L F, Barker D M, Bray J R, Clayton A M, Dalby T, Li D, Payne T J, Saunders F W. The met office global 3-dimensional variational data assimilation scheme[J]. Quart J Roy Meteor Soc, 2000, 126(570):2991-3012.
    [6] Barker D M, Huang W, Guo Y R, Bourgeois A J, Xiao Q N. A three-dimensional(3DVAR) data assimilation system for use with MM5: implementation and initial results[J]. Mon Wea Rev, 2004, 132(4):897-914.
    [7] Bourke W. An efficient one-level primitive equation spectral model[J]. Mon Wea Rev, 1972, 100(9):683-689.
    [8] Bijlsma S J, Hafkensheid L M, Lynch P. Computation of the streamfunction and velocity potential and reconstruction of the wind field[J]. Mon Wea Rev, 1986, 114(8):1547-1551.
    [9] Tangri A C. Computation of streamlines associated with a low latitude cyclone[J]. Indian J Meteor Geophys, 1966, 17:401-406.
    [10] Phillips N A. Geostrophic errors in predicting the Appalachian storm of November 1950[J]. Geophysica, 1958, 6:389-405.
    [11] Brown J A, Neilon J R. Case studies of numerical wind analysis[J]. Mon Wea Rev, 1961, 89(3): 83-90.
    [12] Sangster W E. A method of representing the horizontal pressure force without reduction of pressures to sea level[J]. J Meteor, 1960, 17(2):166-176.
    [13] Sangster W E. An improved technique for computing the horizontal pressure-gradient force at the earth’s surface[J]. Mon Wea Rev, 1987, 115(7): 1358-1368.
    [14] Shukh J, Saha K R. Computation of non-divergent streamfunction and irrotational velocity potential from the observed winds[J]. Mon Wea Rev, 1974, 102(6):419-425.
    [15] Lynch P. Deducing the wind from vorticity and divergence[J]. Mon Wea Rev, 1988, 116(1):86-93.
    [16] Lynch P. Partitioning the wind in a limited domain[J]. Mon Wen Rev, 1989, 117(7):1492-1500.
    [17] Chen Q S, Kuo Y H. A harmonic-sine series expansion and its application to partitioning and reconstruction problems in a limited area[J]. Mon Wea Rev, 1992, 120(1): 91-112.
    [18] Chen Q S, Kuo Y H. A consistency condition for wind-field reconstruction in a limited area and harmonic-cosine series expansion[J]. Mon Wea Rev, 1992, 120(11):2653-2670.
    [19] 朱宗申, 朱国富.有限区域风速场求解流函数和速度势场的有效方案[J]. 应用气象学报, 2008 19(1):10-18. (ZHU Zong-shen, ZHU Guo-fu. An effective method to solve the streamfunction and velocity potential from a wind field in a limited area[J]. Quart J Appl Meteor Sci, 2008, 19(1):10-18. (in Chinese))
    [20] 朱宗申, 朱国富, 张林. 用有限区域风速场准确求解流函数和速度势场的方法[J]. 大气科学, 2009, 33(4):811-824. (ZHU Zong-shen, ZHU Guo-fu, ZHANG Lin. An accurate solution method of stream function and velocity potential from the wind field in a limited area[J]. Chin J Atmos Sci, 2009, 33(4):811-824. (in Chinese))
    [21] 周玉淑, 曹洁, 高守亭. 有限区域风场分解方法及其在台风SAOMEI研究中的应用[J]. 物理学报, 2008, 57(10):6654-6665. (ZHOU Yu-shu, CAO Jie, GAO Shou-ting. The method of decomposing wind field in a limited area and its application to typhoon SAOMEI[J]. Acta Phys Sin, 2008, 57(10):6654-6665. (in Chinese))
    [22] 周玉淑, 曹洁. 有限区域风场的分解和重建[J]. 物理学报, 2010, 59(4):2898-2906. (ZHOU Yu-shu, CAO Jie. Partitioning and reconstruction problem of the wind in a limited region[J]. Acta Phys Sin, 2010, 59(4):2898-2906. (in Chinese))
    [23] Endlich R M. An iterative method for altering the kinematic properties of wind fields[J]. Journal of the Applied Meteorology, 1967, 6(5):837-844.
    [24] Davies-Jones R. On the formulation of surface geostrophic stream function[J]. Mon Wea Rev, 1988, 116(9):1824-1826.
    [25] Li Z J, Chao Y. Computation of the streamfunction and velocity potential for limited and irregular domains[J]. Mon Wea Rev, 2006, 134(11):3384-3394.
    [26] 刘健文, 郭虎, 李耀东, 刘还珠, 吴宝俊. 天气分析预报物理量计算基础[M]. 北京:气象出版社, 2005:249-251. (LIU Jian-wen, GUO Hu, LI Yao-dong, LIU Huan-zhu, WU Bao-jun. The Basis of Weather Analysis and Prediction Physical Quantity Calculation[M]. Beijing: China Meteorologica Press, 2005:249-251. (in Chinese))
    [27] 张文生. 科学计算中的偏微分方程有限差分法[M]. 北京: 高等教育出版社,2006:172-172. (ZHANG Wen-sheng. Finite Difference Methods for Partial Differential Equations in Science Computation[M]. Beijing: Higher Education Press, 2004:172-172. (in Chinese))
    [28] Arakawa A. Computational design for long-term numerical integrations of the equations of atmospheric motion:two dimensional incompressible flow: part Ⅰ[J]. J Comput Phys, 1966, 1(1): 119-143.
    [29] Watterson I G. Decomposition of global ocean currents using a simple iterative method[J]. J Atmos Oceanic Technol, 2001, 18(4):691-703.
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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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