Fast iterative solvers for the discretized incompressible Navier-Stokes equations

International Journal for Numerical Methods in Fluids

Volumn 22, Issue 3, 1996, Pages 195-210

  Vuik, C ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

GMRESR; Incompressible Navier Stokes equations; Iterative solver; Non symmetric linear system; Preconditioning; Vector computer

Indexed keywords

INCOMPRESSIBLE FLOW; ITERATIVE TECHNIQUES; NAVIER-STOKES EQUATIONS;

GMRES; ITERATIVE SOLVERS; NAVIER-STOKES EQUATIONS;

EID: 0029656374     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19960215)22:3<195::aid-fld355>3.0.co;2-4     Document Type: Article

References (26)

1. A. E. Mynett, P. Wesseling, A. Segal and C. G. M. Kassels, 'The ISNaS incompressible Navier-Stokes solver: invariant discretization', Appl. Sci. Res., 48, 175-191 (1991).
2. A. Segal, P. Wesseling, J. Van Kan, C. W. Oosterlee and K. Kassels, 'Invariant discretization of the incompressible Navier-Stokes equations in boundary fitted co-ordinates', Int. j. numer. methods fluids, 15, 411-426 (1992).
3. C. W. Oosterlee, 'Robust multigrid methods for the steady and unsteady incompressible Navier-Stokes equations in general coordinates', Ph.D. Thesis, Delft University of Technology, 1993.
4. C. W. Oosterlee, P. Wesseling, A. Segal and E. Brakkee, 'Benchmark solutions for the incompressible Navier-Stokes equations in general co-ordinates on staggered grids', Int. j. numer. methods fluids, 17, 301-321 (1993).
5. P Wesseling, A Segal, J. J. I. M. Van Kan, C. W. Oosterlee and C. G. M. Kassels, 'Finite volume discretization of the incompressible Navier-Stokes equations in general coordinates on staggered grids', Comput. Fluid Dyn. J., 1, 27-33 (1992).
6. C. Vuik, 'Solution of the discretized incompressible Navier-Stokes equations with the GMRES method', Int. j. numer. methods fluids, 16, 507-523 (1993).
7. G. Segal, K. Vuik and K. Kassels, 'On the implementation of symmetric and antisymmetric periodic boundary conditions for incompressible flow', Int. j. numer. methods fluids, 18, 1153-1165 (1994).
8. M. Zijlema, A. Segal and P. Wesseling, 'Invariant discretization of the k-ε model in general co-ordinates for prediction of turbulent flow in complicated geometries', Comput. Fluids, 24, 209-225 (1995).
9. C. W. Oosterlee and P. Wesseling, 'A multigrid method for an invariant formulation of the incompressible Navier-Stokes equations in general co-ordinates', Commun. Appl. Numer. Methods, 8, 721-734 (1992).
10. C. W. Oosterlee and P. Wesseling, 'A robust multigrid method for a discretization of the incompressible Navier-Stokes equations in general coordinates', Impact Comput. Sci. Eng., 5, 128-151 (1993).
11. C. W. Oosterlee and P. Wesseling, 'Multigrid schemes for time-dependent incompressible Navier-Stokes equations', Impact Comput. Sci. Eng., 5, 153-175 (1993).
12. S. Zeng and P. Wesseling, 'Multigrid solution of the incompressible Navier-Stokes equations in general coordinates', SIAM J. Numer. Anal., 31, 1764-1784 (1994).
13. S. Zeng, C. Vuik and P. Wesseling, 'Solution of the incompressible Navier-Stokes equations in general coordinates by Krylov subspace and multigrid methods', Adv. Comput. Math., 4, 27-49 (1995).
14. Y. Saad and M. H. Schultz, 'GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems', SIAMJ. Sci. Stat. Comput., 7, 856-869 (1986).
15. H. A. Van der Vorst and C. Vuik, 'GMRESR: a family of nested GMRES methods', Numer. Lin. Alg. Appl., 1, 369-386 (1994).
16. C. Vuik, 'Further experiences with GMRESR', Supercomputer, 55, 13-27 (1993).
17. G. de Vahl Davis and I. P. Jones, 'Natural convection in a square cavity: a comparison exercise', Int j. numer. methods fluids, 3, 227-248 (1983).
18. J. A. Meijerink and H. A. Van der Vorst, 'An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix', Math. Comput., 31, 148-162 (1977).
19. H. A. Van der Vorst, 'Iterative solution method for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems', J. Comput. Phys., 44, 1-19 (1981).
20. I. A. Gustafsson, 'Aclass of first order factorization methods', BIT, 18, 142-156 (1978).
21. O. Axelsson and G. Lindskog, On the eigenvalue distribution of a class of preconditioning methods', Numer. Math., 48, 479-498 (1986).
22. H. A. Van der Vorst, 'High performance preconditioning', SIAM J. Sci. Stat. Comput., 10, 1174-1185 (1989).
23. S. C. Eisenstat, 'Efficient implementation of a class of preconditioned conjugate gradient methods', SIAM J. Sci. Stat. Comput., 2, 1-4 (1981).
24. H. A. Van der Vorst and C. Vuik, 'The superlinear convergence behaviour of GMRES', J. Comput. Appl. Math., 48, 327-341 (1993).
25. C. C. Ashcraft and R. G. Grimes, 'On vectorizing incomplete factorization and SSOR preconditioners', SIAM J. Sci. Stat. Comput., 9, 122-151 (1988).
26. E. De Sturler and D. R. Fokkema, 'Nested Krylov methods and preserving the orthogonality', in T. A. Manteuffel and S. F. McCormick (eds), Proc. Sixth Copper Mountain Conf. on Multigrid Methods, NASA Langley Research Center, Hampton, VA, pp. 111-126, 1993.