Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flows in cylindrical geometries

Journal of Computational Physics

Volumn 197, Issue 2, 2004, Pages 759-778

  Blackburn, Hugh M ^a   Sherwin, S J ^b  

^a CSIRO   (Australia)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Cylindrical coordinates; Incompressible flow; Spectral element

Indexed keywords

CYLINDERS (SHAPES); FOURIER SERIES; GALERKIN METHODS; NAVIER STOKES EQUATIONS; VISCOUS FLOW;

CYLINDRICAL COORDINATES; CYLINDRICAL GEOMETRY; FOURIER METHODS; GALERKIN PROJECTIONS; GALERKIN SPECTRAL ELEMENTS; NAVIER-STOKES EQUATION; PRIMITIVE VARIABLES; RADIAL DIRECTION; SPECTRAL ELEMENT; THREE DIMENSIONAL INCOMPRESSIBLE FLOW;

INCOMPRESSIBLE FLOW;

EID: 3242723794     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.02.013     Document Type: Article

References (24)

1. Amon C.H. Spectral element-Fourier method for transitional flows in complex geometries AIAA J. 31 1 1993 42-48
2. Amon C.H. Patera A.T. Numerical calculation of stable three-dimensional tertiary states in grooved-channel flow Phys. Fluids A 1 2 1989 2005-2009
3. Batchelor G.K. Gill A.E. Analysis of the stability of axisymmetric jets J. Fluid Mech. 14 1962 529-551
4. Blackburn H.M. Lopez J.M. Modulated rotating waves in an enclosed swirling flow J. Fluid Mech. 465 2002 33-58
5. Canuto C. Hussaini M.Y. Quarteroni A. Zang T.A. Spectral Methods in Fluid Dynamics 1988 Springer Berlin
6. Deville M.O. Fischer P.F. Mund E.H. High-Order Methods for Incompressible Fluid Flow 2002 Cambridge University Press Cambridge
7. Gerritsma M.I. Phillips T.N. Spectral element methods for axisymmetric Stokes problems J. Comput. Phys. 164 2000 81-103
8. Ghidersa B. Dǔsek J. Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere J. Fluid Mech. 423 2000 33-69
9. Ghizzetti A. Ossicini A. Quadrature Formulae 1970 Academic Press London
10. Guermond J.L. Shen J. Velocity-correction projection methods for incompressible flows SIAM J. Numer. Anal. 41 1 2003 112-134
11. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 1987 Prentice-Hall Englewood Cliffs, NJ
12. Karniadakis G.E. Spectral element-Fourier methods for incompressible turbulent flows Comp. Meth. Appl. Mech. Eng. 80 1990 367-380
13. Karniadakis G.E. Israeli M. Orszag S.A. High-order splitting methods for the incompressible Navier-Stokes equations J. Comput. Phys. 97 2 1991 414-443
14. Karniadakis G.E. Sherwin S.J. Spectral/hp Element Methods for CFD 1999 Oxford University Press Oxford
15. Kovasznay L.I.G. Laminar flow behind a two-dimensional grid Proc. Cambridge Phil. Soc. 44 1948 58-62
16. Kravchenko A.G. Moin P. Shariff K. B-spline method and zonal grids for simulations of complex turbulent flows J. Comput. Phys. 151 1999 757-789
17. Lopez J.M. Marques F. Shen J. An efficient spectral-projection method for the Navier-Stokes equation in cylindrical geometries II. Three-dimensional cases J. Comput. Phys. 176 2002 384-401
18. Oden J.T. Wu W. Legat V. An hp adaptive strategy for the finite element approximations of the Navier-Stokes equations Int. J. Numer. Meth. Fluids 20 1995 831-851
19. Orszag S.A. Patera A.T. Secondary instability of wall-bounded shear flows J. Fluid Mech. 128 1983 347-385
20. Rønquist E.M. Convection treatment using spectral elements of different order Int. J. Numer. Meth. Fluids 22 1996 241-264
21. Shen J. Efficient spectral-Galerkin methods III: polar and cylindrical geometries SIAM J. Sci. Comput. 18 6 1997 1583-1604
22. Strang G. Fix G.J. An Analysis of the Finite Element Method 1973 Prentice-Hall Englewood Cliffs, NJ
23. Tomboulides A.G. Orszag S.A. Numerical investigation of transitional and weak turbulent flow past a sphere J. Fluid Mech. 416 2000 45-73
24. Tuckerman L.S. Divergence-free velocity fields in nonperiodic geometries J. Comput. Phys. 80 1989 403-411