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Applied Mathematics and Mechanics

, Volume 25, Issue 10, pp 1184–1193 | Cite as

Spectral galerkin approximation of couette-taylor flow

  • Wang He-yuan
  • Li Kai-tai
Article

Abstract

Axisymmetric Couette-Taylor flow between two concentric rotating cylinders was simulated numerically by the spectral method. First, stream function form of the Navier-Stokes equations which homogeneous boundary condition was given by introducing Couette flow. Second, the analytical expressions of the eigenfunction of the Stokes operator in the cylindrical gap region were given and its orthogonality was proved. The estimates of growth rate of the eigenvalue were presented. Finally, spectral Galerkin approximation of Couette-Taylor flow was discussed by introducing eigenfunctions of Stokes operator as basis of finite dimensional approximate subspaces. The existence, uniquence and convergence of spectral Galerkin approximation of nonsingular solution for the steady-state Navier-Stokes equations are proved. Moreover, the error estimates are given. Numerical result is presented.

Key words

Navier-Stokes equation Couette-Taylor flow spectral approximation Stokes operator 

Chinese Library Classification

O357.1 O241.82 

2000 Mathematics Subject Classification

65J15 47H15 65M60 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2004

Authors and Affiliations

  • Wang He-yuan
    • 1
    • 2
  • Li Kai-tai
    • 2
  1. 1.Department of Mathematics and PhysicsLiaoning Institute of TechnologyLiaoningP.R. China
  2. 2.School of SciencesXi'an Jiaotong UniversityXi'anP.R. China

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