Comparison of pressure correction smoothers for multigrid solution of incompressible flow

International Journal for Numerical Methods in Fluids

Volumn 25, Issue 4, 1997, Pages 393-405

  Gjesdal, Thor ^a   Lossius, Magni Elén Hope ^a,b  

^a CHRISTIAN MICHELSEN RESEARCH AS   (Norway)

^b HAV Kurs og Kompetensesenter   (Norway)

Author keywords

Incompressible Navier Stokes equations; Multigrid methods; Pressure correction methods

Indexed keywords

COMPRESSIBLE FLOW; COMPUTATIONAL FLUID DYNAMICS; CONVERGENCE OF NUMERICAL METHODS; NAVIER STOKES EQUATIONS; PRESSURE;

INCOMPRESSIBLE FLOW; LID DRIVEN CAVITY FLOW; MULTIGRID METHODS; PRESSURE CORRECTION SMOOTHERS; UNDERRELAXATION PARAMETER;

ALGORITHMS;

ALGORITHM; GRID; INCOMPRESSIBLE FLOW; NAVIER-STOKES EQUATIONS; PRESSURE;

EID: 0031205528     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19970830)25:4<393::aid-fld554>3.0.co;2-i     Document Type: Review

References (30)

1. S. Sivaloganathan and G. J. Shaw, 'An efficient non-linear multigrid procedure for the incompressible Navier-Stokes equations', Int. j. numer. methods fluids, 8, 417-440 (1988).
2. W. Shyy and C.-S. Sun, 'Development of a pressure-correction/staggered grid based multigrid solver for incompressible recirculating flow', Comput. Fluids, 22, 51-76 (1993).
3. C. Becker, J. H. Ferziger, M. Perić and G. Scheurer, 'Finite volume multigrid solutions of the two-dimensional incompressible Navier-Stokes equations', in W. Hackbusch (ed.), Robust Multi-Grid Methods, NNFM Vol. 23, Vieweg, Braunschweig, 1988, pp. 37-47.
4. F. S. Lien and M. A. Leschziner, 'Multigrid acceleration for recirculating laminar and turbulent flows computed with a non orthogonal, collocated finite volume scheme', Comput. Methods Appl. Mech. Eng., 118, 351-371 (1994).
5. K. M. Smith, W. K. Cope and S. P. Vanka, 'Multigrid procedure for three-dimensional flows on non-orthogonal collocated grids', Int. j. numer. methods fluids, 17, 887-904 (1993).
6. P. Johansson and L. Davidson, 'A full multigrid method applied to turbulent flow using the SIMPLEC algorithm together with a collocated arrangement, in P. W. Hemker and P. Wesseling (eds), Multigrid Methods IV. Proc. Fourth Eur. Multigrid Conf, ISNM Vol. 116, Birkhäuser, Basle, 1994, pp. 245-256.
7. Ch. Arakawa, A. O. Demuren, W. Rodi and B. Schönung, 'Application of multigrid method for the coupled and decoupled solution of the incompressible N-S equations', in M. Deville (ed.) Proc. 7th GAMM Conf. on Numerical Methods in Fluid Mechanics, NNFM Vol, 20, Vieweg, Braunschweig, 1988, pp. 1-8.
8. S. V. Patankar and D. B. Spalding, 'A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows', Int. J. Heat Mass Transfer, 15, 1787-18806 (1972).
9. J. P. Van Doormal and G. D. Raithby, 'Enhancements of the SIMPLE method for predicting incompressible fluid flows', Numer Heat Transfer, 7, 147-163 (1984).
10. T. Gjesdal, M. E. H. Lossius and R. Teigland, 'Multigrid solution of incompressible flow using pressure correction smoothers', in P. A. Thibault and D. M. Bergeron (eds), Proc. Third Ann. Conf. of the CFD Society of Canada, Vol. 1, Combustion Dynamics, Ltd., Medicine Hat, Alberta, 1995, pp. 39-45.
11. J. H. Ferziger and M. Perić, Computational Methods for Fluid Dynamics, Springer, Berlin, 1996.
12. S. W. Armfield, 'Ellipticity, accuracy and convergence of the discrete Navier-Stokes equations', J. Comput. Phys., 114, 176-184 (1994).
13. C. M. Rhie and W. L. Chow, 'Numerical study of the turbulent flow past an airfoil with trailing edge separation', AIAA J., 21, 1525-1532 (1983).
14. A. Brandt, 'Multi-level adapative solutions to boundary-value problems', Math. Comput., 31, 333-390 (1977).
15. A. J. Chorin, 'Numerical solution of the Navier-Stokes equations', Math. Comput., 23, 351-354 (1968).
16. R. Temam, 'Sur l'approximation de la solution des equations de Navier-Stokes par le méthode de pas fractionnaire', Arch. Rat. Mech. Anal., 32, 135-153 (1969).
17. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.
18. G. J. Shaw and S. Sivaloganathan, 'The SIMPLE pressure-correction method as a nonlinear smoother', in S. F. McCormick (ed.), Multigrid Methods: Theory, Applications, and Supercomputing, LNPAM Vol. 110, Marcel Dekker, New York, 1988, pp. 579-596.
19. G. J. Shaw and S. Sivaloganathan, 'On the smoothing properties of the SIMPLE pressure-correction algorithm', Int. j. numer. methods fluids, 8, 441-461 (1988).
20. P. Wesseling, An Introduction to Multigrid Methods, Wiley, Chichester, 1992.
21. A. Brandt, 'Guide to multigrid development', in W. Hackbusch and U. Trottenberg (eds), Multigrid Methods, LNM Vol. 960, Springer, Berlin, 1982, pp. 220-312.
22. W. Hackbusch, Multigrid Methods and Applications, CM Vol. 4, Springer, Berlin, 1985.
23. P. W. Hemker, 'On the order of prolongations and restrictions in multigrid procedures', J. Comput. Appl. Math., 32, 423-429 (1990).
24. B. Koren, 'A robust upwind discretization for advection, diffusion and source terms', in C. B. Vreugdenhill and B. Koren (eds), Numerical Methods for Advection-Diffusion Problems, NNFM Vol. 45, Vieweg, Braunschweig, 1993, pp. 117-138.
25. W. Hunsdorfer, B. Koren, M. van Loon and J. G. Verwer, 'A positive finite-difference advection scheme', J. Comput. Phys., 117, 35-46 (1995).
26. W. Heinrichs, 'Defect correction for the advection diffusion equation', Comput. Methods Appl. Mech. Eng., 119, 191-197 (1994).
27. A. Brandt and I. Yavneh, 'Accelerating multigrid convergence and high-Reynolds recirculating flows', SIAM J. Sci. Comput., 14, 607-626 (1993).
28. M. Perić, R. Kessler and G. Scheurer, 'Comparison of finite-volume numerical methods with staggered and colocated grids', Comput. Fluids, 16, 389-403 (1988).
29. U. Ghia, K. N. Ghia and C. T. Shin, 'High-Re solutions for incompressible Navier-Stokes equations and a multi-grid method', J. Comput. Phys., 48, 387-411 (1982).
30. N. Ramanan and G. M. Homsy, 'Linear stability of lid-driven cavity flow', Phys. Fluids, 6, 2690-2701 (1994).