1. Simulation de la turbulence par la méthode des grandes échelles. 2. Résolution d'équations de la mécanique des fluides par la méthode des inconnues incrémentales

Poullet, Pascal

Directeur de thèse : Temam, Roger

Membres du jury : Temam, Roger ; Bruneau, Charles-Henri ; Cancelier, Claudy ; Laminie, Jacques ; Scheurer, Bruno

Thèses d'Orsay, no. 455 (1996) , 218 p.

Export
Comment citer

@phdthesis{BJHTUP11_1996__0455__A1_0,
     author = {Poullet, Pascal},
     title = {1. {Simulation} de la turbulence par la m\'ethode des grandes \'echelles. 2. {R\'esolution} d'\'equations de la m\'ecanique des fluides par la m\'ethode des inconnues incr\'ementales},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {455},
     year = {1996},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_1996__0455__A1_0/}
}

TY  - BOOK
AU  - Poullet, Pascal
TI  - 1. Simulation de la turbulence par la méthode des grandes échelles. 2. Résolution d'équations de la mécanique des fluides par la méthode des inconnues incrémentales
T3  - Thèses d'Orsay
PY  - 1996
IS  - 455
PB  - Université de Paris-Sud Centre d'Orsay
UR  - http://www.numdam.org/item/BJHTUP11_1996__0455__A1_0/
LA  - fr
ID  - BJHTUP11_1996__0455__A1_0
ER  -

%0 Book
%A Poullet, Pascal
%T 1. Simulation de la turbulence par la méthode des grandes échelles. 2. Résolution d'équations de la mécanique des fluides par la méthode des inconnues incrémentales
%S Thèses d'Orsay
%D 1996
%N 455
%I Université de Paris-Sud Centre d'Orsay
%U http://www.numdam.org/item/BJHTUP11_1996__0455__A1_0/
%G fr
%F BJHTUP11_1996__0455__A1_0

Poullet, Pascal. 1. Simulation de la turbulence par la méthode des grandes échelles. 2. Résolution d'équations de la mécanique des fluides par la méthode des inconnues incrémentales. Thèses d'Orsay, no. 455 (1996), 218 p. http://numdam.org/item/BJHTUP11_1996__0455__A1_0/

Bibliographie
Cité par

[BAU93] G. Baudier. Simulation de la turbulence par la méthode des grandes echelles. Technical report, Commissariat à l'Energie Atomique CEA/DMA/MCN, 07/1993.

[BER93] J.P. Bertoglio. Simulation numérique d'ecoulements turbulents. Technical report, Ecole de Printemps à Carcans-Maubuisson, 05/1993.

[BLC94] A. De La Bourdonnaye, B. Larrouturou, and R. Carpentier. On the derivation of the modified equation for the analysis of linear numerical methods. Technical Report 94-26, Centre d'Enseignement et de Recherche en Modélisation, Informatique et Calcul Scientifique, 01/1994. | MR | Numdam

[CL82] J.P. Chollet and M. Lesieur. Parametrization of small scales of threedimensional isotropic turbulence utilizing spectral closures. Journal of Atmosphere Science, (38): 2747-2757, 1982. | DOI

[DEL85] P. Delorme. Simulation Numérique en Dynamique de la Turbulence Homogène Compressible. PhD thesis, Université de Poitiers, 10/1985.

[HIR92] C. Hirsch. Fundamentals of Numerical Discretization, volume 1 of Numerical Computation of Internal and External Flows. John Wiley & Sons, 1992. | Zbl

[KOL41a] A.N. Kolmogorov. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C.R. Acad. Sci. URSS, 30, 1941. | MR | JFM

[KOL41b] A.N. Kolmogorov. On degeneration of isotropic turbulence in an incompressible viscous fluid. C.R. Acad. Sci. URSS, 32, 1941. | MR | Zbl

[LES73] D.C. Leslie. Developments in the theory of turbulence. Oxford Science Publications, 1973. | MR | Zbl

[LEV90] R.J. Leveque. Numerical Methods for conservation laws. Birkhäuser, 1990. | MR | Zbl

[McC92] W.D. Mccomb. The Physics of Fluid Turbulence. Oxford Science Publications, 1992. | MR | Zbl

[ML91] O. Metais and M. Lesieur. Spectral Large-Eddy Simulation of isotropic and stably-stratified turbulence, submitted to Journal of Fluid Mechanics, 1991. | MR | Zbl

[NGML92] A. Silveira Neto, D. Grand, O. Metais, and M. Lesieur. A numerical investigation of the coherent structures of turbulence behind a backward-facing step. Journal of Fluid Mechanics, 1992. | Zbl

[PS95] P. Poullet and M. Sancandi. Simulation de la turbulence par la méthode des grandes echelles. Technical Report 2796, Commissariat a l'Energie Atomique, CEL-V/DMA/MCN, 94195 Villeneuve St Georges, 1995.

[ROY8O] P. Roy. Résolution des équations de Navier-Stokes par un schéma de haute précision en espace et en temps. La Recherche Aérospatiale, 6:373-385, 1980. | MR | Zbl

[SAG] P. Sagaut. Modèles de viscosité turbulente. Communication Personnelle, ONERA CERT.

[VGKZ92] A.W. Vreman, B.J. Geurts, J.G.M. Kuerten, and P.J. Zandbergen. A finite volume approach to Large Eddy Simulation of compressible, homogeneous, isotropic, decaying turbulence. Int. J. Numerical Methods in Fluids, 15:799-816, 1992. | Zbl | DOI

[WH74] R.F. Warming and B.J. Hyett. The modified equation approach to the stability and accuracy analysis of finite-difference methods. Journal of Computational Physics, 14:159-179, 1974. | MR | Zbl | DOI

[ARN51] W.E. Arnoldi. The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Applied Mathematics, 9:17-29, 1951. | MR | Zbl

[BPX90] J.H. Bramble, J.E. Pasciak, and J. Xu. Parallel multilevel preconditioners. Mathematics of Computation, 55(191):1-22, 1990. | MR | Zbl

[BS90] P.N. Brown and Y. Saad. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput., 11 (3):450-481, 1990. | MR | Zbl | DOI

[CEA64] J. Cea. Approximation variationnelle des problèmes aux limites. Ann. Inst. Fourier, 14:345-444, 1964. | MR | Zbl | Numdam | DOI

[CJ84] T.F. Chan and K.R. Jackson. Nonlinearly preconditioned Krylov subspace methods for discrete Newton algorithms. SIAM J. Sci. Stat. Comput., 5(3):533-542, 1984. | MR | Zbl | DOI

[CHE93] J.P. Chehab. Méthode des Inconnues Incrémentales. Applications au calcul des bifurcations. PhD thesis, Université Paris-XI, 01/1993.

[CMT94] M. Chen, A. Miranville, and R. Temam. Incremental Unknowns in finite difference in three space dimensions. Computational and Applied Mathematics, 14(3):217, 1995. | Zbl | MR

[CT91] M. Chen and R. Temam. Incremental Unknowns for solving partial differential equations. Numer. Math., 59:255-271, 1991. | MR | Zbl | DOI

[CT93] M. Chen and R. Temam. Incremental Unknowns in finite differences: Condition number of the matrix. SIAM J. Matrix Anal. Appl., 14(2):432-455, 1993. | MR | Zbl | DOI

[DES82] R.S. Dembo, S.C. Eisenstat, and T. Steihaug. Inexact Newton methods. SIAM J. Numer. Anal., 19(2):400-408, 1982. | MR | Zbl | DOI

[DS83a] R.S. Dembo and T. Steihaug. Truncated-Newton algorithms for large-scale unconstrained optimization. Mathematical Programming, 26:190-212, 1983. | MR | Zbl

[DS83b] J.E. Dennis and R.B. Schnabel. Numerical methods for unconstrained optimization and nonlinear equations. Prentice-Hall, Englewood Cliffs NJ, 1983. | MR | Zbl

[FLE76] R. Fletcher. Conjugate Gradient methods for indefinite systems. Lecture Notes in Mathematics, 506:73-89, 1976. | MR | Zbl

[FLE88] C.A.J. Fletcher. Computational techniques for fluid dynamics, volume 1 of Springer Series in Computational Physics. Springer-Verlag, 1988. | Zbl

[GL90] G.H. Golub and Van Loan. Matrix computations. Johns Hopkins Series in the Mathematical Sciences. The Johns Hopkins University Press, 1990. | MR | Zbl

[GOY94] O. Goyon. Résolution numérique de problèmes stationnaires et évolutifs non linéaires par la méthode des Inconnues Incrémentales. PhD thesis, Université Paris-XI, 12/1994.

[GP95] O. Goyon and P. Poullet. Numerical resolutions using Incremental Unknowns methods of steady-state Navier-Stokes like equations. Prépublication de l'Université PARIS-SUD, 1995. 95-87.

[GRMM92] M.A. Gomes-Ruggiero, J.M. Martinez, and A.C. Moretti. Comparing algorithms for solving sparse nonlinear systems of equations. SIAM J. Sci. Stat. Comput., 13(2):459-483, 1992. | MR | Zbl | DOI

[HAC85] W. Hackbusch. Multigrid methods and applications. Springer-Verlag, 1985. | MR

[HIR92] C. Hirsch. Fundamentals of Numerical Discretization, volume 1 of Numerical Computation of Internal and External Flows. John Wiley & Sons, 1992. | Zbl

[MED95] T. Tachim Medjo. Sur les formulations vitesse-vorticité pour les équations de Navier-Stokes en dimension deux - Implémentation des Inconnues Incrémentales Oscillantes dans les équations de Navier-Stokes et de réaction-diffusion. PhD thesis, Université Paris-XI, 06/ 1995.

[NAS84] S.G. Nash. Newton-type minimization via Lanczos method. SIAM J. Numer. Anal., 21(4):770-788, 1984. | MR | Zbl | DOI

[PAS92] F. Pascal. Méthodes de Galerkin non linéaires en discrétisation par éléments finis et pseudo-spectrale. Application à la Mécanique des Fluides. PhD thesis, Université Paris-XI, 01/ 1992.

[SON89] P. Sonneveld. Cgs : A fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 10:36-52, 1989. | MR | Zbl | DOI

[SS86] Y. Saad and M.H. Schultz. A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7(3):856-869, 1986. | MR | Zbl | DOI

[TEM66] R. Temam. Sur l'approximation des équations de Navier-Stokes. C. R. Acad. Sci. Paris, Sér. A, 262:219-221, 1966. | MR | Zbl

[TEM84] R. Temam. Navier-Stokes Equations. North-Holland, 1984. | MR | Zbl

[TEM90] R. Temam. Inertial manifolds and multigrid methods. SIAM J. Math. Anal., 21(1):154-178, 1990. | MR | Zbl | DOI

[VOR82] H.A. Van Der Vorst. A vectorizable variant of some ICCG methods. SIAM J. Sci. Stat. Comput., 3(3):350-356, 1982. | MR | Zbl | DOI

[VOR92] 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(2):631-644, 1992. | MR | Zbl | DOI

[WES82] P. Wesseling. Theoretical and practical aspects of a multigrid method. SIAM J. Sci. Stat. Comput., 3:387-407, 1982. | MR | Zbl | DOI

[YSE86] H. Yserantant. On the multi-level splitting of finite element spaces. Numerische Mathematik, 49:379-412, 1986. | MR | Zbl

[BIG74] A. Ben-Israel and T.N.E. Greville. Generalized Inverses theory and applications. Pure & Applied Mathematics. John Wiley & Sons, 1974. | MR | Zbl

[BJ90] C.H. Bruneau and C. Journon. An efficient scheme for solving partial differential equations. Journal of Computational Physics, 89(2):389-413, 1990. | Zbl | DOI

[BRA92] R. Bramley. An orthogonal projection algorithm for linear Stokes problems. Technical Report 1190, Center for Supercomputing Research and Development, University of Illinois, Urbana, 1992.

[CC87] K. Cahouet and J. Chabard. Some fast 3d finite element solvers for generalized Stokes problem. Technical Report HE-41/87.03, Electricité De France, D.E.R., 6 quai Watier, 78400 Chatou, 1987. | MR | Zbl

[CLT95] C. Calgaro, J. Laminie, and R. Temam. Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element methods. Prépublication de l'Université PARIS-SUD, 1995. 95-77. | MR | Zbl

[DAU92] O. Daube. Resolution of the 2d Navier-Stokes equation in velocity-vorticity form by means of an influence matrix technique. Journal of Computational Physics, 103:402-414, 1992. | MR | Zbl | DOI

[DAV83] R.W. Davis. Finite difference methods for fluid flow. In J. Noye and C. Fletchet, editors, Computational Techniques and Applications : CT.AC-83. North-Holland, 1983. | MR | Zbl

[FLE88] C.A.J. Fletcher. Computational Techniques for Fluid Dynamics, volume 2 of Springer Series in Computational Physics. Springer-Verlag, 1988. | MR | Zbl

[FMT88] C. Foias, O. Manley, and R. Temam. Modelling of the interaction of small and large eddies in two-dimensional turbulent flow. Math. Mod. and Num. Anal., 22:93-114, 1988. | MR | Zbl | Numdam

[GAR92] S. Garcia. Etude algébrique et numérique de la méthode des Inconnues Incrémentales. PhD thesis, Université Paris-XI, 06/1992.

[GCLU84] P.M. Gresho, S.T. Chan, R.L. Lee, and C.D. Upson. A modified finite element method for solving the time-dependant, incompressible Navier-Stokes equations, part 2: applications. Int. J. Numerical Methods in Fluids, 4:619-640, 1984. | Zbl | DOI

[GGH90] J.W. Goodrich, K. Gustafson, and K. Halasi. Hopf bifurcation in the driven cavity. Journal of Computational Physics, 90:219-261, 1990. | MR | Zbl | DOI

[GGS82] U. Ghia, K.N. Ghia, and C.T. Shin. High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48:387-411, 1982. | Zbl | DOI

[GIR76] V. Girault. A combined finite element and Marker And Cell method for solving Navier-Stokes equations. Numer. Math., 26:39-59, 1976. | MR | Zbl

[GOY94] O. Goyon. Résolution Numérique de problèmes stationnaires et évolutifs non linéaires par la méthode des Inconnues Incrémentales. PhD thesis, Université Paris-XI, 12/1994.

[GS87] P.M. Gresho and R.L. Sani. On pressure boundary conditions for the Navier-Stokes equations. Int. J. Numerical Methods in Fluids, 7:1111-1145, 1987. | Zbl | DOI

[HIR92] C. Hirsch. Fundamentals of Numerical Discretization, volume 1 of Numerical Computation of Internal and External Flows. John Wiley & Sons, 1992. | Zbl

[HW65] F. Harlow and J. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surfaces. Phys. Fluids, 8(12):2181-2189, 1965. | MR | Zbl | DOI

[LLM90] C. Liu, Z. Liu, and S. Mccormick. Multigrid methods for flow transition in a planar channel. In Computational Physics, Plenary Lectures and Expanded Selected Papers from the IMACS 1st International Conference, University of Colorado at Boulder, USA, 1990. North-Holland. | MR | Zbl

[PT83] R. Peyret and T.D. Taylor. Computational Methods for Fluid Flow. Springer-Verlag, 1983. | MR | Zbl | DOI

[SHE87] J. Shen. Résolution numérique des équations de Stokes et Navier-Stokes par les méthodes spectrales. PhD thesis, Université Paris-XI, 1987.

[SHE91] J. Shen. Hopf bifurcation of the unsteady regularized driven cavity flow. Journal of Computational Physics, 95:228-245, 1991. | Zbl | DOI

[TEM84] R. Temam. Navier-Stokes Equations. North-Holland, 1984. | MR | Zbl