HUANG Wei, GUO Ben-yu. Fully Discrete Jacobi-Spherical Harmonic Spectral Method for Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2008, 29(4): 409-431.
Citation: HUANG Wei, GUO Ben-yu. Fully Discrete Jacobi-Spherical Harmonic Spectral Method for Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2008, 29(4): 409-431.

Fully Discrete Jacobi-Spherical Harmonic Spectral Method for Navier-Stokes Equations

  • Received Date: 2007-10-19
  • Rev Recd Date: 2008-03-07
  • Publish Date: 2008-04-15
  • A fully discrete Jacobi-spherical harmonic spectral method was provided for the Navier-Stokes equations in a ball.Its stability and convergence were proved.Numerical results show the efficiency of this approach.The proposed method is also applicable to other problems in spherical geometry.
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  • [1]
    Girault V,Raviart P A.Finite Element Approximation of the Navier-Stokes Equations[M].Lecture Notes in Mathematics.794.Berlin: Springer-Verlag,1979.
    [2]
    GUO Ben-yu. Difference method for fluid dynamics-numerical solution of primitive equations[J].Scientia Sinica,Series A,1981,24(3):297-312.
    [3]
    郭本瑜.偏微分方程的差分方法[M].北京:科学出版社,1988.
    [4]
    Roache P J.Computational Fluid Dynamics[M].2nd Ed. Albuquerque:Hermosa Publishers,1976.
    [5]
    Téman R.Navier-Stokes Equations[M].Amsterdam: North-Holland,1977.
    [6]
    Bernardi C, Maday Y.Spectral methods[A].In:Ciarlet P G,Lions J L,Eds.Handbook of Numerical Analysis.Vol 5.Techniques of Scientific Computing[C].Amsterdam:Elsevier,1997,209-486.
    [7]
    Boyd J P.Chebyshev and Fourier Spectral Methods[M].Berlin:Springer-Verlag,1989.
    [8]
    Canuto C, Hussaini M Y,Quarteroni A,et al.Spectral Methods in Fluid Dynamics[M].Berlin:Springer-Verlag,1988.
    [9]
    Funaro P.Polynomial Approximations of Differential Equations[M].Berlin:Springer-Verlag,1992.
    [10]
    Gottlieb D, Orszag S A.Numerical Analysis of Spectral Methods: Theory and Applications[M].Philadelphia: SIAM-CBMS, 1977.
    [11]
    GUO Ben-yu.Spectral Methods and Their Applications[M].Singapore:World Scientific,1998.
    [12]
    GUO Ben-yu. Spectral method for Navier-Stokes equations[J].Scientia Sinica, Series A,1985,28(11):1139-1153.
    [13]
    GUO Ben-yu, MA He-ping. Combined finite element and pseudospectral method for the two-dimensional evolutionary Navier-Stokes equations[J].SIAM J Numer Anal,1993,30(4):1066-1083. doi: 10.1137/0730055
    [14]
    Hald O H. Convergence of Fourier methods for Navier-Stokes equations[J].J Comput Phys,1981,40(2):305-317. doi: 10.1016/0021-9991(81)90212-6
    [15]
    Maday Y, Quarteroni A. Spectral and pseudospectral approximations of the Navier-Stokes equations[J].SIAM J Numer Anal,1982,19(4):761-780. doi: 10.1137/0719053
    [16]
    MA He-ping, GUO Ben-yu. Combined finite element and pseudospectral method for the three-dimensional Navier-Stokes equations[J].Chinese Annals of Mathematics,Series B,1992,13(3):350-367.
    [17]
    Boyd J P. The choice of spectral functions on a sphere for boundary and eigenvalue problems: a comparison of Chebyshev, Fourier and associated Legendre expansion[J].Mon Weather Rev,1978,106(8):1184-1191. doi: 10.1175/1520-0493(1978)106<1184:TCOSFO>2.0.CO;2
    [18]
    Efstathiou G. A model of supernova feedback in galaxy formation[J].Mon Not R Astron Soc,2000,317(3):697-719. doi: 10.1046/j.1365-8711.2000.03665.x
    [19]
    Haltiner G J, Williams R T.Numerical Prediction and Dynamical Meteorology[M].New York: John Wiley & Sons, 1980.
    [20]
    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].J Comput Phys,1992,102(1):211-224. doi: 10.1016/S0021-9991(05)80016-6
    [21]
    Bramble J H, Pasciak J E.A boundary parametric approximation to linearized scalar potential magnetostatic field problem[J].Appl Numer Math,1985,1(6):493-514. doi: 10.1016/0168-9274(85)90034-0
    [22]
    CAO Wei-ming, GUO Ben-yu. A pseudospectral method for vorticity equations on spherical surface[J].Acta Math Appl Sinica,1997,13(2):176-187. doi: 10.1007/BF02015139
    [23]
    GUO Ben-yu. A spectral method for the vorticity equation on the surface[J].Math Comp,1995,64(211):1067-1079.
    [24]
    GUO Ben-yu, CAO Wei-ming. A spectral method for the fluid flow with low Mach number on the spherical surface[J].SIAM J Numer Anal,1995,32(6):1764-1777. doi: 10.1137/0732080
    [25]
    GUO Ben-yu. Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations[J].J Math Anal Appl,2000,243(2):373-408.
    [26]
    GUO Ben-yu, HUANG Wei.Mixed Jacobi-spherical harmonic spectral method for Navier-Stokes equations[J].Appl Numer Math,2007,57(8):939-961. doi: 10.1016/j.apnum.2006.09.003
    [27]
    GUO Ben-yu, WANG Li-lian.Jacobi interpolation approximations and their applications to singular differential equations[J].Adv in Comput Math,2001,14(3):227-276. doi: 10.1023/A:1016681018268
    [28]
    GUO Ben-yu, WANG Li-lian. Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces[J].J Approx Theory,2004,128(1):1-41. doi: 10.1016/j.jat.2004.03.008
    [29]
    Chorin A J. The numerical solution of the Navier-Stokes equations for an incompressible fluid[J].Bull Amer Math Soc,1967,73(6):928-931. doi: 10.1090/S0002-9904-1967-11853-6
    [30]
    Chorin A J. Numerical solution of the Navier-Stokes equations[J].Math Comp,1968,22(104):745-762. doi: 10.1090/S0025-5718-1968-0242392-2
    [31]
    Lions J L. On the numerical approximation of some equations arising in hydrodynamics[A].In:Birkhoff G, Varga R S, Eds.Numerical Solution of Field Problems in Continuum Physics, SIAM-AMS Proceedings Ⅱ[C].Providence, Rhode Island:AMS,1970,11-23.
    [32]
    Courant R, Hilbert D.Methods of Mathematical Physics[M].Vol 1.New York: Interscience Publisher, 1953.
    [33]
    Bergh J, Lfstrm J.Interpolation Spaces,an Introduction[M].Berlin: Springer-Verlag,1976.
    [34]
    Dumas G, Leonard A.A divergence-free spectral expansions method for three-dimensional flow in spherical-gap geometries[J].J Comput Phys,1994,111(2):205-219. doi: 10.1006/jcph.1994.1056
    [35]
    Friedman A.Partial Differential Equations[M].New York: Holt, Rinehart and Winston, 1969.
    [36]
    Adams R A.Sobolev Spaces[M].New York: Academic Press, 1975.
    [37]
    陈恕行.偏微分方程概论[M].北京:人民教育出版社,1981.
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