# American Institute of Mathematical Sciences

March  2009, 11(2): 315-345. doi: 10.3934/dcdsb.2009.11.315

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

 1 Department of Mathematics, Shanghai Normal University, Shanghai 200234, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai E-institute for Computational Science, China, China

Received  November 2007 Revised  July 2008 Published  December 2008

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.
Citation: Ben-Yu Guo, Yu-Jian Jiao. Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 315-345. doi: 10.3934/dcdsb.2009.11.315
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