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Volume 12 Issue 1

Jan.  1995

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1995 >  12(1): 109-113

Some Splitting Methods for Equations of Geophysical Fluid Dynamics

  • 1.

    LASG,InstituteofAtmosphericPhysics,ChineseAcademyofSciences,LASG,InstituteofAtmosphericPhysics,ChineseAcademyofSciences


doi: 10.1007/BF02661293

  • In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.
  • [1] Lin Wantao, Ji Zhongzhen, Wang Bin, 2002: A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 699-704.  doi: 10.1007/s00376-002-0009-9
    [2] Wang Bin, Ji Zhongzhen, 1993: An Improved Splitting Method, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 447-452.  doi: 10.1007/BF02656969
    [3] Yi Zengxin, T. Warn, 1987: A NUMERICAL METHOD FOR SOLVING THE EVOLUTION EQUATION OF SOLITARY ROSSBY WAVES ON A WEAK SHEAR, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 43-54.  doi: 10.1007/BF02656660
    [4] Ji Zhongzhen, Wang Bin, 1997: Multispectrum Method and the Computation of Vapor Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 563-568.  doi: 10.1007/s00376-997-0074-1
    [5] Xixun ZHOU, Bing XIE, Hua ZHANG, Jingyi HE, Qi CHEN, 2022: Decomposition of Fast and Slow Cloud Responses to Quadrupled CO2 Forcing in BCC–AGCM2.0 over East Asia, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 2188-2202.  doi: 10.1007/s00376-022-1441-7
    [6] Wu Beiying, Lu Daren, 1984: REMOTE SENSING OF RAINFALL PARAMETERS BY LASER SCINTILLATION CORRELATION METHOD-COMPLETE EQUATION AND NUMERICAL SIMULATION, ADVANCES IN ATMOSPHERIC SCIENCES, 1, 19-39.  doi: 10.1007/BF03187613
    [7] Qian Yongfu, 1988: THE LOCAL SPLINE VERTICAL INTERPOLATION METHOD OF TEMPERATURE AND GEOPOTENTIAL HEIGHT FIELDS AND THE TIME-DEPENDENT DIFFERENCE FORM OF THE HYDROSTATIC EQUATION, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 159-170.  doi: 10.1007/BF02656778
    [8] Gao Shouting, Liu Kunru, 1990: Introduction of the Direct Method by Illustrating Schr?dinger Equation and Its Application to Wave-Wave Striking Interaction, ADVANCES IN ATMOSPHERIC SCIENCES, 7, 186-191.  doi: 10.1007/BF02919156
    [9] Gao Shouting, 1991: A-B Hybrid Equation Method of Nonlinear Bifurcation in Wave-Flow Interaction, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 165-174.  doi: 10.1007/BF02658092
    [10] XUE Hai-Le, SHEN Xue-Shun, CHOU Ji-Fan, 2013: A Forecast Error Correction Method in Numerical Weather Prediction by Using Recent Multiple-time Evolution Data, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1249-1259.  doi: 10.1007/s00376-013-2274-1
    [11] Gao Shouting, Lei Ting, 2000: Streamwise Vorticity Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 339-347.  doi: 10.1007/s00376-000-0027-4
    [12] Baofeng JIAO, Lingkun RAN, Na LI, Ren CAI, Tao QU, Yushu ZHOU, 2023: Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 856-873.  doi: 10.1007/s00376-022-1435-5
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    [16] Liu Guifu, 1996: Introduction to an Invariant Quantity Method, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 59-66.  doi: 10.1007/BF02657028
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    • Manuscript History

    Manuscript received: 10 January 1995
    Manuscript revised: 10 January 1995
    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

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    Some Splitting Methods for Equations of Geophysical Fluid Dynamics

    • 1. LASG,InstituteofAtmosphericPhysics,ChineseAcademyofSciences,LASG,InstituteofAtmosphericPhysics,ChineseAcademyofSciences
    • Manuscript received: 1995-01-10
    • Manuscript revised: 1995-01-10

    Abstract: In this paper, equations of atmospheric and oceanic dynamics are reduced to a kind of evolutionary equation in operator form, based on which a conclusion that the separability of motion stages is relative is made and an issue that the tractional splitting methods established on the physical separability of the fast stage and the slow stage neglect the interaction between the two stages to some extent is shown. Also, three splitting patterns are summed up from the splitting methods in common use so that a comparison between them is carried out. The comparison shows that only the improved splitting pattern (ISP) can be in second order and keep the interaction well. Finally, the applications of some splitting methods on numerical simulations of typhoon tracks made clear that ISP owns the best effect and can save more than 80% CPU time.

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