Acta Mechanica Sinica

, Volume 18, Issue 1, pp 53–65 | Cite as

Retrospective time integral scheme and its applications to the advection equation

  • Feng Guolin
  • Dong Wenjie
  • Yang Peicai
  • Cao Hongxing
  • Chou Jifan


To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.

Key words

time integration memorization numerical weather prediction difference scheme advection equation 


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  1. 1.
    Shen MY, Niu XL, Zheng ZB. The there-point fifth-order accurate generalized compact scheme and its applications.Acta Mechanica Sinica, 2001, 17(2): 142–150MathSciNetCrossRefGoogle Scholar
  2. 2.
    Robert A. A stable numerical integration scheme for the primitive meteorological equations.Atmos-Ocean, 1981, 19(1): 35–46Google Scholar
  3. 3.
    O'Brien JJ. Time Integration Schemes Advanced Physical Oceanographic Numerical Modeling. Amsterdam: Reidel Press, 1986. 155–164Google Scholar
  4. 4.
    Wang RQ, Shen YQ. Some weight-type high-resolution difference schemes and their applications.Acta Mechanica Sinica, 1999, 15(4): 313–324CrossRefGoogle Scholar
  5. 5.
    Bates R. A global multi-level atmospheric model using a vector semi-Lagrangian difference scheme. Part I: Adiabatic formulation.Mon Wea Rev, 1993, 121: 244–263CrossRefGoogle Scholar
  6. 6.
    Zhang HX, Guo C, Zong, WG. Problems about gird and height order schemes.Acta Mechanica Sinica, 1999, 31 (4): 398–405 (in Chinese)Google Scholar
  7. 7.
    Wang B. A time-saving explicit scheme for numerical integration.Chinese Science Bulletin, 1993, 38(3): 230–234MATHGoogle Scholar
  8. 8.
    Egger J. Volume conservation in phase space: A fresh look at numerical integration schemes.Mon Wea Rev, 1996, 124(9): 1955–1964CrossRefGoogle Scholar
  9. 9.
    Cao HX. Self-memorization equation in atmospheric motion.Science in China, Series B, 1993, 36(7): 845–855MathSciNetGoogle Scholar
  10. 10.
    Cao HX, Feng GL. Self-memorial model of climate prediction and its preliminary application.Chinese J Comput Phys, 1999, 16 (2): 206–210 (in Chinese)Google Scholar
  11. 11.
    Rivest, C, Staniforth A, Robert R. Spurious resonant response of semi-Lagrangian discretization to orographic forcing.Mon Wea Rev, 1994, 122: 366–376CrossRefGoogle Scholar
  12. 12.
    ECMWF. ECMWF Forecast Model. ECMWF Research Department, 1987Google Scholar
  13. 13.
    Haltiner GJ. Numerical Weather Prediction. New York: John Wiley & Son Inc, 1971. 78–101Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2002

Authors and Affiliations

  • Feng Guolin
    • 1
    • 4
  • Dong Wenjie
    • 2
  • Yang Peicai
    • 2
  • Cao Hongxing
    • 3
  • Chou Jifan
    • 1
  1. 1.Department of Meteorological SciencesLanzhou UniversityLanzhouChina
  2. 2.Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina
  3. 3.Chinese Academy of Meteorological SciencesBeijingChina
  4. 4.Mathematics and Physics CollegeYangzhou UniversityYangzhouChina

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