×

The Fourier-Chebyshev spectral method for solving two-dimensional unsteady vorticity equations. (English) Zbl 0757.76047

Summary: We propose a mixed method for solving the two-dimensional unsteady vorticity equations by using the Fourier-spectral approximation in the periodic direction and Chebyshev-spectral approximation in the non- periodic direction. Some numerical results are given, which are compared with those of other methods. Stability of the schemes and the optimal rate of convergence are proved.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D99 Incompressible viscous fluids
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Roache, P. J., Computational fluid dynamics (1976), Hermosa: Hermosa Albuquerque, NM
[2] Raviart, P. A., Approximation numerique des phénomènes de diffusion convection, (Method d’éléments finis en mechanics des fluids, Cours a l’école d’été d’analyse numerique (1979)) · Zbl 0241.65065
[3] Guo, B. Y., Finite Differences Methods for Partial Differential Equations (1988), Science Press: Science Press Beijing
[4] Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A., Spectral Method in Fluid Dynamics (1988), Springer-Verlag: Springer-Verlag Bedlin · Zbl 0658.76001
[5] Murdok, J. W., AIAA Paper 86-0434 (1986), (unpublished)
[6] Ingham, D. B., (Proc. R. Soc. London A, 402 (1985)), 109
[7] Moin, P.; Kim, J., J. Fluid Mech., 118, 341 (1982)
[8] Macaraeg, M. G., J. Comput. Phys., 62, 297 (1986)
[9] Guo, B. Y.; Xiong, Y. S., J. Comput. Phys., 84, 259 (1989)
[10] Canuto, C.; Maday, Y.; Quarteroni, A., Numer. Math., 44, 201 (1984)
[11] Guo, B. Y.; Cao, W. M., Acta Math. Appl. Sin., 7, 257 (1991)
[12] Canuto, C.; Quarteroni, A., Math. Comput., 38, 67 (1982)
[13] Adams, R. A., Sobolev spaces (1975), Academic Press: Academic Press New York · Zbl 0186.19101
[14] Ma, H. P.; Guo, B. Y., J. Comput. Math., 6, 48 (1988)
[15] Maday, Y.; Quarteroni, A., Numer. Math., 37, 321 (1981)
[16] Quarteroni, A., Jpn. J. Appl. Math., 1, 173 (1984)
[17] (1949)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.