Methodes iteratives pour les fluides incompressibles
Keywords:
modelling, finite element, iterative methods, preconditionner, incompressible flowsAbstract
This paper presents an overview of different iterative methods Conjugate gradient (CG), Biconjugate gradient (BfCG), conjugate gradient squared (CGS), Biconjugate gradient stabilized (BfCGSTAB), transpose{ree quasi minimal residual (TFQMR), full orthogonal method (FOM) et Generalized minimal residual (GMRES) for solving finite element systems of Navier-Stokes incompressible flows. To accelerate convergence of those methods, preconditio11ner based on incomplete Gauss factorisation (fLU) is used. The accent is put on the necessity to renumber the unknowns to guaranty the convergence of the iterative methods. The importance of a variable stop criterion of iterative methods for each Newton-Raphso/1 step is underlined.
Downloads
References
[COC 94] B. COCHEUN, "Methodes Asymptotiques-Numeriques pour le calcul non-lineaire
geometrique des structures elastiques", Habilitation a diriger des recherches, Universite de
Metz, 1994.
[DAM 90] N. DAMIL, M. POTIER-FERRY, "A new method to compute perturbed bifurcations:
Application to the buckling of imperfect elastic structures", Int. J. Engineering Sciences,
vol. 28,704-719, (1990).
[DHA 84] G. DHATT, G. TOUZOT, Une presentation de Ia methode des eliments finis.
Maloine, 1984.
[DHA 95] G. DHATT, M. FAFAR, "Mecanique non-lineaire", Cours IPSI, Paris, 1995.
[FRE 93] R. W. FREUND, "A Transpose-Free quasi-minimal residual algorithm for the nonhermitian
linear systems", SIAM J. Sci. Statist. Comput., vol. 14, pp. 470-482, 1993.
[HAD 95] S.HADJI, "Methode de resolution pour les fluides incompressibles", these de
doctoral, Universite de Technologie de Compiegne, 1995.
[HAD 97] S.HADJI, G. DHATT, "Asymptotic-Newton method for solving incompressible
flows", Int. J. Numer. Methods fluids, a paraitre.
[HOW 90] D. HOWARD, W. M. CONNOLLEY, J. S. ROLLETI, "Unsymmetric conjugate
gradient methods and sparse direct methods in finite element flow simulation", /111. J.
Num. Methods fluids, vol. 10,925-945, 1990.
[MEl 81] J. A. MEUERINK, H. A. VANDER VORST, "Guidelines for the usage of incomplete
decompositions in solving sets of linear equations as they occur in practical problems",
Journal of Computational Physics, 44, 134-155, 1981.
[SAA 86] Y. SAAD, M. H. SCHULTZ, "GMRES : a generalized minimal residual algorithm for
solving nonsymetric linear systems", SIAM J. Sci. Statist. Comput., vol. 7, pp. 856-869,
[SON 89] P. SONNEVELD, "CGS, a fast Lanczos-type solver for nonsymmetric linear systems",
SIAM J. Sci. Statist. Comput., vol. 10, pp. 36-52, 1989.
[STO] M. STORI, N. NIGROT, S. IDELSOHN , "Stabilising equal-order interpolations for mixed
formulations of Navier-Stokes equations via SUPG method", Research Report,
Universidad Nacional dellitoral and CONICET, Argentina.
[VAN 92] H. A. VANDER VORST, "BI-CGSTAB: a fast and smoothly converging variant of
BI-CG for the solutions of nonsymmetric linear systems", SIAM J. Sci. Statist. Comput.,
vol. 13, pp. 631-644, 1992.
