Advanced Search
Article Contents

Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations


doi: 10.1007/s00376-001-0048-7

  • Based on the forced dissipative nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipative nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.
  • [1] Lin Wantao, Ji Zhongzhen, Wang Bin, 2001: Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 413-417.  doi: 10.1007/BF02919320
    [2] 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
    [3] Ji Zhongzhen, Lin Wantao, Yang Xiaozhong, 2001: Problems of Nonlinear Computational Instability in Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 397-403.  doi: 10.1007/BF02919318
    [4] LIN Wantao, WANG Chunhua, CHEN Xingshu, 2003: A Comparative Study of Conservative and Nonconservative Schemes, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 810-814.  doi: 10.1007/BF02915406
    [5] LIU Yongming, CAI Jingjing, 2006: On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 809-814.  doi: 10.1007/s00376-006-0809-4
    [6] Mu Mu, Zeng Qingcun, 1991: Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 1-10.  doi: 10.1007/BF02657360
    [7] Liu Yongming, 1999: Nonlinear Stability of Zonally Symmetric Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 107-118.  doi: 10.1007/s00376-999-0007-2
    [8] Liu Yongming, Mu Mu, 1992: A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 337-345.  doi: 10.1007/BF02656943
    [9] Liu Yongming, Mu Mu, 1994: Arnol’d’s Second Nonlinear Stability Theorem for General Multilayer Quasi-geostrophic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 36-42.  doi: 10.1007/BF02656991
    [10] He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100.  doi: 10.1007/BF02656998
    [11] Li Yang, Mu Mu, Wu Yonghui, 2000: A Study on the Nonlinear Stability of Fronts in the Ocean on a Sloping Continental Shelf, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 275-284.  doi: 10.1007/s00376-000-0009-6
    [12] Mu Mu, Guo Huan, Wang Jiafeng, LiYong, 2000: The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 375-390.  doi: 10.1007/s00376-000-0030-9
    [13] JIANG Zhina, 2006: Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 775-783.  doi: 10.1007/s00376-006-0775-x
    [14] Li Yang, Mu Mu, 1996: On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 203-216.  doi: 10.1007/BF02656863
    [15] Mu Mu, Wu Yonghui, Tang Mozhi, Liu Haiyan, 1999: Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 569-580.  doi: 10.1007/s00376-999-0032-1
    [16] Ren Shuzhan, 1994: Note on the Symmetric Stability of Quasi-Homogeneous and Incompressible Rotating Ocean, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 74-78.  doi: 10.1007/BF02656996
    [17] Ren Shuzhan, 1991: Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 129-136.  doi: 10.1007/BF02658089
    [18] Luo Dehai, Li Jianping, 2001: Interaction between a Slowly Moving Planetary-Scale Dipole Envelope Rossby Soliton and a Wavenumber-Two Topography in a Forced Higher Order Nonlinear Schr dinger Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 239-256.  doi: 10.1007/s00376-001-0017-1
    [19] 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
    [20] Ji Zhongzhen, Wang Bin, 1993: Constructions and Applied Examinations of a Kind of Square-Conservative Schemes in High Precision in the Time Direction, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 315-324.  doi: 10.1007/BF02658137

Get Citation+

Export:  

Share Article

Manuscript History

Manuscript received: 10 July 2001
Manuscript revised: 10 July 2001
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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations

  • 1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese ,Academy of Sciences,Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese ,Academy of Sciences,Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese ,Academy of Sciences,Beijing 100029

Abstract: Based on the forced dissipative nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipative nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return