Highly energy-conservative finite difference method for the cylindrical coordinate system

Journal of Computational Physics

Volumn 181, Issue 2, 2002, Pages 478-498

  Fukagata, Koji ^a,b   Kasagi, Nobuhide ^a  

^a UNIVERSITY OF TOKYO   (Japan)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

Advection; Body force; Cylindrical coordinate system; Energy conservation; Finite difference method; Incompressible flow; Pipe flow; Singularity

Indexed keywords

ENERGY CONSERVATION; INCOMPRESSIBLE FLOW; MESH GENERATION; NUMERICAL METHODS;

BODY FORCES; CARTESIAN COORDINATE; CYLINDRICAL COORDINATE SYSTEMS; CYLINDRICAL COORDINATES; ENERGY; FINITE-DIFFERENCE METHODS; INTERPOLATION SCHEMES; NUMERICAL TESTS; SECOND ORDERS; SINGULARITY;

FINITE DIFFERENCE METHOD;

EID: 0037144932     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7138     Document Type: Article

References (22)

1. M. Lesieur and O. Métais, New trends in large-eddy simulations of turbulence, Annu. Rev. Fluid Mech. 28, 45 (1996).
2. U. Piomelli, Large-eddy simulations: Where we stand, in Advances in DNS/LES edited by C. Liu, Z. Liu, and L. Sakell (Greyden Press, Columbus, 1997), p. 93.
3. N. Kasagi, Progress in direct numerical simulation of turbulent transport and its control, Int. J. Heat Fluid Flow 19, 125 (1998).
4. P. Moin and K. Mahesh, Direct numerical simulation: A tool in turbulence research, Annu. Rev. Fluid Mech. 30, 539 (1998).
5. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications (Soc. for Industr. & Appl. Math. Philadelphia, 1977).
6. F. H. Harlow and J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 8, 2182 (1965).
7. S. A. Piacsek and G. P. Williams, Conservation properties of convection difference schemes, J. Comput. Phys. 6,392 (1970).
8. Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 143, 90 (1998), doi:10.1006/jcph.1998.5962.
9. T. Kajishima, Finite-difference method for convective terms using non-uniform grid, Trans. JSME/B 65(633), 103 (1999) (in Japanese).
10. F. E. Ham, F. S. Lien, and A. B. Strong, A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids, J. Comput. Phys. 177, 117 (2002), doi:10.1006/jcph.2002.7006.
11. J. G. M. Eggels, F. Unger, M. H. Weiss, J. Westerweel, R. J. Adrian, R. Friedrich, and F. T. M. Nieuwstadt, Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment, J. Fluid Mech. 268, 175 (1994).
12. K. Akselvoll and P. Moin, Large Eddy Simulation of Turbulent Confined Coannular Jets and Turbulent Flow over a Backward Facing Step, Stanford Univ. Report TF-63 (1995).
13. R. Verzicco and P. Orlandi, A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates, J. Comput Phys. 123, 402 (1996), doi:10.1006/jcph.1996.0033.
14. P. Orlandi and M. Fatica, Direct simulations of turbulent flow in a pipe rotating about its axis, J. Fluid Mech. 343, 43 (1997).
15. G. S. Constantinescu and S. K. Lele, A new method for accurate treatment of flow equations in cylindrical coordinates using series expansions, in CTR Annual Research Briefs 2000, edited by P. Moin, W. C. Reynolds, and N. N. Mansour (Center for Turbulence Research, NASA Ames and Stanford Univ. Press, Stanford, CA, 2000), p. 199.
16. K. Mohseni and T. Colonius, Numerical treatment of polar coordinate singularities, J. Comput. Phys. 157, 787 (2000), doi:10.1006/jcph. 1999.6382.
17. O. Vasilyev, High order finite difference schemes on non-uniform meshes with good conservation properties, J. Comput. Phys. 157, 746 (2000), doi:10.1006/jcph.1999.6398.
18. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Springer-Verlag, Berlin, 1989), p. 475.
19. P. R. Spalart, R. D. Moser, and M. M. Rogers, Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions, J. Comput. Phys. 96, 297 (1991).
20. M. M. Rai and P. Moin, Direct numerical simulations of turbulent flow using finite difference schemes, J. Comput. Phys. 96, 15 (1991).
21. J. K. Dukowicz and A. S. Dvinsky, Approximate factorization as a higher order splitting for the implicit incompressible flow equations, J. Comput. Phys. 102, 336 (1992).
22. τ = 590, Phys. Fluids 11,