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Journal of Shanghai University >

2018 , Vol. 24 >Issue 4: 602 - 608

DOI: https://doi.org/10.12066/j.issn.1007-2861.1847

Research Articles

Mixed Legendre-spherical harmonic spectral method for solving Navier-Stokes equations

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  • College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2016-08-30

  Online published: 2018-08-31

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Abstract

A fully discrete mixed Legendre-spherical harmonic spectral method was proposed for the Navier-Stokes equations in a domain between two concentric balls. Legendre orthogonal approximation is used in the radial direction, and spherical harmonic orthogonal approximation in other directions. The forward difference quotient is used for time derivative. Numerical results show efficiency of this approach.

Key words： spectral method; Navier-Stokes Equations; domain between two concentric balls

Cite this article

SONG Yang, HUANG Wei . Mixed Legendre-spherical harmonic spectral method for solving Navier-Stokes equations[J]. Journal of Shanghai University, 2018 , 24(4) : 602 -608 . DOI: 10.12066/j.issn.1007-2861.1847

References

[1] Haltiner G J, Williams R T . Numerical prediction and dynamical meteorology[M]. 2nd ed. New York: John Wiley & Sons, 1980.
[2] Williamson D L, Drake J B, Hack J J , et al. A standard test set for numerical approximations to the shallow water equations in spherical geometry[J]. Journal of Computational Physics, 1992,102(1):211-224.
[3] Cao W M, Guo B Y . A pseudospectral method for vorticity equations on spherical surface[J]. Acta Mathematicae Applicatae Sinica, 1997,13(2):176-187.
[4] Guo B Y . A spectral method for the vorticity equation on the surface[J]. Mathematics and Computation, 1995,64(211):1067-1079.
[5] Guo B Y, Cao W M . A spectral method for the fluid flow with low Mach number on the spherical surface[J]. SIAM Journal on Numerical Analysis, 1995,32(6):1764-1777.
[6] Guo B Y, Huang W . Mixed Jacobi-spherical harmonic spectral method for Navier-Stokes equations[J]. Applied Numerical Mathematics, 2007,57(8):939-961.
[7] 黄伟, 郭本瑜 . Navier-Stokes方程的全离散Jacobi-球面调和谱方法[J]. 应用数学和力学, 2008,29(4):409-431.
[8] 夏文杰, 黄伟 . 求解Fisher型方程的混合Legendre-球面调和谱方法[J]. 应用数学与计算数学学报, 2014,28(1):26-32.
[9] 邓红梅, 黄伟 . 二阶精度混合Legendre-球面调和拟谱方法求解Fisher型方程[J]. 上海大学学报(自然科学版), 2015,21(3):331-335.
[10] Girault V, Raviart P A . Finite element appraximation of the Navier-Stokes equations[M]. Berlin: Springer-Verlag, 1979.
[11] Guo B Y . Difference method for fluid dynamics-numerical solution of primitive equations[J]. Scientia Sinica, 1981,24(3):297-312.
[12] 郭本瑜 . 偏微分方程的差分解法 [M]. 北京: 科学出版社, 1988.
[13] Roache P J . Computational fluid dynamics[M]. 2nd ed. Albuquerque: Hermosa Publishers, 1985.
[14] Teman R. Navier-Stokes equations [M]. Amsterdam: North-Holland Publishing Company, 1977.
[15] Hald O H . Convergence of Fourier methods for Navier-Stokes equations[J]. Journal of Computational Physics, 1981,40(2):305-317.
[16] Maday Y, Qaurteroni A . Spectral and pseudospectral approximations of the Navier-Stokes equations[J]. SIAM Journal on Numerical Analysis, 1982,19(4):761-780.
[17] Guo B Y . Spectral method for Navier-Stokes equations[J]. Scientia Sinica Series A: Mathematical, Physical, Astronomical and Technical Sciences, 1985,28:1139-1153.
[18] Ma H P, Guo B Y . Combined finite element and pseudospectral method for the three-dimensional Navier-Stokes equations[J]. Chinese Anuals of Mathematics Series B, 1992,13(3):350-367.
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