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Mixed spherical harmonic-generalized Laguerre spectral method is proposed for the Navier-Stokes equations set in exterior domain. Its stability and convergence are proved. Numerical results demonstrate the efficiency of this approach. Some results on the spherical harmonic-generalized Laguerre approximation are established, which play an important role in numerical analysis in spectral method in spherical geometry.

Mixed spherical harmonic-generalized Laguerre spectral method for the Navier–Stokes equations