Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations

Pages: 315 - 345, Volume 11, Issue 2, March 2009

doi:10.3934/dcdsb.2009.11.315       Abstract        Full Text (402.6K)       Related Articles

Ben-Yu Guo - Department of Mathematics, Shanghai Normal University, Shanghai 200234, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai E-institute for Computational Science, China (email)
Yu-Jian Jiao - Department of Mathematics, Shanghai Normal University, Shanghai 200234, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai E-institute for Computational Science, China (email)

Abstract: In this paper, we investigate the mixed generalized Laguerre-Fourier spectral method and its applications to exterior problems of partial differential equations of fourth order. Some basic results on the mixed generalized Laguerre-Fourier orthogonal approximation are established, which play important roles in designing and analyzing various spectral methods for exterior problems of fourth order. As an important application, a mixed spectral scheme is proposed for the stream function form of the Navier-Stokes equations outside a disc. The numerical solution fulfills the compressibility automatically and keeps the same conservation property as the exact solution. The stability and convergence of proposed scheme are proved. Numerical results demonstrate its spectral accuracy in space, and coincide with the analysis very well.

Keywords:  Mixed generalized Laguerre-Fourier spectral method, exterior problems of fourth order, Navier-Stokes equations
Mathematics Subject Classification:  65N35, 41A10, 76D05, 35J35

Received: November 2007;      Revised: July 2008;      Published: December 2008.