SPECTRAL GALERKIN APPROXIMATION OF COUETTE-TAYLOR FLOW  

作　　者：王贺元 李开泰 

机构地区：[1]Department of Mathematics and Physics Liaoning Institute of Technology [2]School of Sciences Xi'an Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2004年第10期1184-1193,共10页应用数学和力学（英文版）

基　　金：theNationalKeyBasicResearchSpecialFoundationofChina (G1 990 3 2 80 107),theNationalNaturalScienceFoundationofChina ( 1 0 1 0 1 0 2 0 )

摘　　要：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.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.

关 键 词：Navier-Stokes equation Couette-Taylor flow spectral approximation Stokes operator 

分 类 号：O241.8[理学—计算数学]