Accelerated Multigrid High Accuracy Solution of the Convection-Diffusion Equation with High Reynolds Number

Numerical Methods for Partial Differential Equations

Volumn 13, Issue 1, 1997, Pages 77-92

  Zhang, Jun ^a  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002545264     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199701)13:1<77::AID-NUM6>3.0.CO;2-J     Document Type: Article

References (42)

1. M. M. Gupta, "High accuracy solutions of incompressible Navier-Stokes equations," J. Comput. Phys. 93, 343 (1991).
2. A. Brandt and I. Yavneh, "On multigrid solution of high-Reynolds incompressible entering flows," J. Comput. Phys. 101, 151 (1992).
3. A. Brandt and I. Yavneh, "Accelerated multigrid convergence and high-Reynolds recirculating flows," SIAM J. Sci. Comput. 14, 607 (1993).
4. P. M. de Zeeuw and E. J. van Asselt, "The convergence rate of multigrid algorithms applied to the convection-diffusion equation," SIAM J. Sci. Stat. Comput. 6, 492 (1985).
5. P. M. de Zeeuw, "Matrix-dependent prolongations and restrictions in a blackbox multigrid solver," J. Comput. Appl. Math. 33, 1 (1990).
6. A. Reusken, "Multigrid with matrix-dependent transfer operators for convection-diffusion problems," in Multigrid Methods IV, Proc. of 4th European Multigrid Conference, Amsterdam, P. W. Hemker and P. Wesseling, Eds., Birkhauser Verlag, Basel, 1994, p. 267.
7. A. Reusken, "Fourier analysis of a robust multigrid method for convection-diffusion equations," Numer. Math. 71, 365 (1995).
8. H. C. Elman and G. H. Golub, "Iterative method for cyclically reduced non-self-adjoint linear systems," Math. Comp. 54, 671 (1990).
9. M. M. Gupta, R. P. Manohar, and J. W. Stephenson, "A fourth order, cost effective and stable finite difference scheme for the convection-diffusion equation," in Numer. Properties & Methodologies in Heat Transfer., Proc. 2nd National Symp., Hemisphere Pub. Co., Washington, DC, 1983, p. 201.
10. M. M. Gupta, R. P. Manohar, and J. W. Stephenson, "A single cell high order scheme for the convection-diffusion equation with variable coefficients," Int. J. Numer. Methods Fluids 4, 641 (1984).
11. 4 finite difference approximation to operators of Navier-Stokes type," J. Comput. Phys. 85, 390 (1989).
12. M. Li, T. Tang, and B. Fornberg, "A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations," Int. J. Numer. Methods Fluids 30, 1137 (1995).
13. W. F. Spotz and G. F. Carey, "High-order compact scheme for the steady stream-function vorticity equations," Int. J. Numer. Methods Eng. 38, 3497 (1995).
14. I. Alias and K. Burrage, "A high accuracy defect-correction multigrid method for the steady incompressible Navier-Stokes equations," J. Comput. Phys. 114, 227 (1994).
15. M. M. Gupta, "A fourth-order Poisson solver," J. Comput. Phys. 55, 166 (1984).
16. S. Schaffer, "High order multi-grid methods," Math. Comp. 43, 89 (1984).
17. M. M. Gupta, J. Kouatchou, and J. Zhang, "Comparison of 2nd and 4th order discretizations for the multigrid Poisson solver," J. Comput. Phys., to appear.
18. A. Brandt, "Multi-level adaptive solution to boundary-value problems," Math. Comp. 31, 333 (1977).
19. A. Brandt, "Guide to multigrid development," in Multigrid Methods, W. Hackbusch and U. Trottenberg, Eds., Lecture Notes in Math., Vol. 960, Springer-Verlag, New York, 1981, p. 220.
20. W. Briggs, A Multigrid Tutorial, SIAM, Philadelphia, 1987.
21. P. Wesseling, An Introduction to Multigrid Methods, John Wiley & Sons, Chichester, 1992.
22. W. Auzinger and H. J. Stetter, "Defect correction and multigrid iteration," in Multigrid Methods, W. Hackbusch and U. Trottenberg, Eds., Lecture Notes in Math., Vol. 960, Springer-Verlag, New York, 1981, p. 327.
23. W. Auzinger, "Defect corrections for multigrid solutions of the Dirichlet problem in general domains," Math. Comp. 48, 471 (1987).
24. W. Hackbusch, "On multigrid iterations with defect correction," in Multigrid Methods, W. Hackbusch and U. Trottenberg, Eds., Lecture Notes in Math., Vol. 960, Springer-Verlag, New York, 1981, p. 461.
25. P. W. Hemker, "Mixed defect correction iteration for the accurate solution of the convection-diffusion equation," in Multigrid Methods, W. Hackbusch and U. Trottenberg, Eds., Lecture Notes in Math., Vol. 960, Springer-Verlag, New York, 1981, p. 485.
26. N. G. Wright and P. H. Gaskell, "An efficient multigrid approach to solving highly recirculating flows," Computers & Fluids 24, 63 (1995).
27. A. Brandt and I. Yavneh, "Inadequacy of first-order upwind difference scheme for some recirculating flows," J. Comput. Phys. 93, 128 (1991).
28. A. Brandt and V. Mikulinsky, "On recombining iterants in multigrid algorithms and problems with small islands," SIAM J. Sci. Comput. 16, 20 (1995).
29. J. Zhang, "Acceleration of five-point Red-Black Gauss-Seidel in multigrid for two dimensional Poisson equation," Appl. Math. Comput., to appear.
30. J. Zhang, "Residual scaling techniques in multigrid, I: equivalence proof," Appl. Math. Comput., to appear.
31. W. Schönauer, Scientific Computing on Vector Computers, North-Holland, Amsterdam, 1987.
32. R. Weiss, Convergence Behavior of Generalized Conjugate Gradient Methods, Ph.D. Thesis, University of Karlsrushe, Germany, 1990.
33. L. Zhou and H. F. Walker, "Residual smoothing techniques for iterative methods," SIAM J. Sci. Comput. 15, 297 (1994).
34. Y. Saad and M. H. Schultz, "GMRES: a generalized minimal residual method for solving nonsymmetric linear systems," SIAM J. Sci. Stat. Comput. 7, 856 (1986).
35. C. Lanczos, "Solution of systems of linear equations by minimized iterations," J. Res. Nat. Bur. Stand. 49, 33 (1952).
36. P. Sonneveld, "CGS, a fast Lanczos-type solver for nonsymmetric linear systems," SIAM J. Sci. Stat. Comput. 10, 36 (1989).
37. H. A. van der Vorst, "BI-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems," SIAM J. Sci. Stat. Comput. 13, 631 (1992).
38. R. W. Freund, "A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems," SIAM J. Sci. Comput. 14, 470 (1993).
39. H. F. Walker, "Residual smoothing and peak/plateau behavior in Krylov subspace methods," Appl. Numer. Math. 19, 279 (1995).
40. 2-norm," SIAM J. Numer. Anal. 31, 1695 (1994).
41. A. E. Berger, J. M. Solomon, M. Ciment, S. H. Leventhal, and B. C. Weinberg, "Generalized OCI schemes for boundary layer problems," Math. Comp. 35, 659 (1980).
42. J. Zhang, "Minimal residual smoothing in multi-level iterative method," Appl. Math. Comput., to appear.