ANZIAM J. 46(E) pp.C918--C934, 2005.

A comparison of staggered and non-staggered grid Navier--Stokes solutions for the 8:1 cavity natural convection flow

S. Armfield

R. Street

(Received 17 November 2004, revised 14 July 2005)

Abstract

The Navier--Stokes equations may be discretised using finite-volume schemes on non-staggered or on staggered grids. The staggered grid is known to prevent pressure oscillations that may occur on the non-staggered grid; however, this is at the expense of increased code complexity. Non-staggered grid schemes that employ iterative time integration are known to require the use of some form of explicit correction in the construction of the Poisson pressure correction equation. We investigate a fractional-step pressure-correction non-staggered scheme and compare it to a similar fractional-step staggered grid scheme for bifurcated natural convection flow in an 8:1 cavity.

Download to your computer

Authors

S. Armfield
School of Aerospace, Mechanical & Mechatronic Engineering, Sydney University, Sydney, Australia. mailto:armfield@aeromech.usyd.edu.au
R. Street
Environmental Fluid Mechanics Laboratory, Stanford University, Stanford, California 94305-4020, USA

Published September 12, 2005. ISSN 1446-8735

References

  1. K. J. Bathe (ed). First MIT Meeting on Computational Solid and Fluid Mechanics, vols 1 and 2, MIT Elsevier, New York, June 2001.
  2. M. A. Christon, P. M. Gresho and S. B. Sutton. Computational predictability of time-dependent natural convection flows in enclosures (incuding a benchmark solution). International Journal for Numerical Methods in Fluids, 40:951--1144, 2002. http://www3.interscience.wiley.com/cgi-bin/jissue/99019470
  3. S. W. Armfield. Finite difference solutions of the Navier--Stokes equations on staggered and non-staggered grids. Computers and Fluids,20:1--17, 1991. http://www3.interscience.wiley.com/cgi-bin/abstract/89011177
  4. J. C. Strikewerda. Finite difference methods for the Stokes and Navier--Stokes equations. SIAM J. Sci. Stat. Comput., 5:56--68, 1984.
  5. S. Abdallah. Numerical solutions of the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid, 1. J. Computational Physics, 70:182--192, 1987.
  6. G. Schneider and M. Raw. Control volume finite-element method for heat transfer and fluid flow using collocated variables-1. Computational procedure. Numerical Heat Transfer, 11:363--390, 1987.
  7. C. M. Rhie and W. L. Chow. A numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA-82-0988, 1982.
  8. S. W. Armfield and R. Street. Fractional step methods for the Navier--Stokes equations on non-staggered grids. ANZIAM J., 42(E):C134--C156, 2000. http://anziamj.austms.org.au/V42/CTAC99/Armf.
  9. S. W. Armfield and R. Street. An analysis and comparison of the time accuracy of fractional step methods for the Navier--Stokes equations on staggered grids. Int. J. Numerical Methods in Fluids, 38:255--282, 2002.
  10. S. W. Armfield and R. Street. The fractional step method for the Navier--Stokes equations on staggered grids: the accuracy of three variations. Journal of Computational Physics, 153:660-665, 1999.
  11. S. W. Armfield and R. Street. The pressure accuracy of fractional-step methods for the Navier--Stokes equations on staggered grids. ANZIAM J. , 44(E):C20--C39, 2003. http://anziamj.austms.org.au/V44/CTAC2001/Armf
Copyright Austral. Mathematical Soc.; prepared September 12, 2005, from Armf.tex with anziamje.sty (v2.3h)