Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (11): 1334-1341.

• 论文 • 上一篇    下一篇

ANALYSIS AND APPLICATION OF ELLIPTICITY OF STABILITY EQUATIONS ON FLUID MECHANICS

李明军, 高智   

  1. LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China
  • 收稿日期:2001-08-21 修回日期:2003-05-28 出版日期:2003-11-18 发布日期:2003-11-18
  • 基金资助:
    the National Natural Science Foundation of China (10032050);the National 863 Program Foundation of China (2002AA633100)

ANALYSIS AND APPLICATION OF ELLIPTICITY OF STABILITY EQUATIONS ON FLUID MECHANICS

LI Ming-jun, GAO Zhi   

  1. LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China
  • Received:2001-08-21 Revised:2003-05-28 Online:2003-11-18 Published:2003-11-18
  • Supported by:
    the National Natural Science Foundation of China (10032050);the National 863 Program Foundation of China (2002AA633100)

摘要: By using characteristic analysis of the linear and nonlinear parabolic stability equations ( PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub- characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic., respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

Abstract: By using characteristic analysis of the linear and nonlinear parabolic stability equations ( PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub- characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic., respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

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