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Theses

DÉVELOPPEMENT D'UNE MÉTHODE IMPLICITE SANS MATRICE POUR LA SIMULATION 2D-3D DES ÉCOULEMENTS COMPRESSIBLES ET FAIBLEMENT COMPRESSIBLES EN MAILLAGES NON-STRUCTURÉS

Abstract : The computation of steady flows can be considered efficient not only if a steady state is reached for a reduced CPU time but also if a low memory storage is used in this process; besides, for complex industrial applications involving grids with very large numbers of points this latter requirement may become especially critical. The same comment holds of course for unsteady flows, now classically computed by a dual time-stepping approach in which a steady-state with respect to the dual time must be reached at each physical time-step. The strong need for low-storage efficient implicit treatments has led to the development of so-called matrix-free (MF) methods. In the particular applications the CEA is interested in, namely the simulation of buoyant multi-component reactive flow in a nuclear reactor containment, the methods should be versatile enough to deal with flow regimes ranging from nearly incompressible to highly compressible. It has been known for more than a decade now that a proper preconditioning, so-called low-Mach preconditioning, of the equations governing compressible flows enables the application of schemes initially developed for compressible flows simulation to the incompressible regime. The present thesis demonstrates how it is possible to preserve a matrix-free implicit treatment for flows at all speeds when the implicit stage involves a preconditioning matrix ; the intrinsic efficiency of the matrix-free implicit scheme coupled with either Point Jacobi (PJ) or Symmetric Gauss-Seidel (SGS) relaxation procedures is studied using a Von Neumann analysis, comparisons with standard block implicit schemes are then carried out. Eventually, the matrix-free implicit method is implemented within the unstructured Code CAST3M and it is applied to the modeling of a Tee junction at low-Mach number regime. The matrix-free implicit scheme is shown to be a competitive alternative for the simulation of compressible and quasi-incompressible flows on unstructured grids.
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https://pastel.archives-ouvertes.fr/tel-00356821
Contributor : Thibaud Kloczko <>
Submitted on : Wednesday, January 28, 2009 - 5:21:50 PM
Last modification on : Tuesday, April 28, 2020 - 11:28:10 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 7:41:42 PM

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  • HAL Id : tel-00356821, version 1

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Thibaud Kloczko. DÉVELOPPEMENT D'UNE MÉTHODE IMPLICITE SANS MATRICE POUR LA SIMULATION 2D-3D DES ÉCOULEMENTS COMPRESSIBLES ET FAIBLEMENT COMPRESSIBLES EN MAILLAGES NON-STRUCTURÉS. Modélisation et simulation. Arts et Métiers ParisTech, 2006. Français. ⟨NNT : 2006ENAM0007⟩. ⟨tel-00356821⟩

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