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Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (4): 453-476 .doi: https://doi.org/10.1007/s10483-008-0404-1

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Fully discrete Jacobi-spherical harmonic spectral method for Navier-Stokes equations

HUANG Wei, GUO Ben-yu   

    1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China;
    3. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, P. R. China;
    4. Division of Computational Science of E-Institute of Shanghai Universities, Shanghai 200234, P. R. China
  • Received:2007-10-19 Revised:2008-02-25 Online:2008-04-18 Published:2008-04-18
  • Contact: HUANG Wei

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Abstract: A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results show efficiency of this approach. The proposed method is also applicable to other problems in spherical geometry.

Key words: fully discrete Jacobi-spherical harmonic spectral method, Navier-Stokes equations in a ball, mixed coordinates

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