Kloczko, Thibaud (2006) A matrix-free implicit treatment for all speed flows on unstructured grids. PhD thesis Mécanique, ENSAM 2006ENAM0007.
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. 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.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.
| Item Type: | PhD Thesis (PhD) |
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| Thesis Supervisor: | Lerat, Alain |
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| Date: | March 2006 |
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| Board of examiners: | Guillard, Hervé and Dick, Erik and Dubroca, Bruno and Beccantini, Alberto and Corre, Christophe and Lerat, Alain |
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| Ecole Doctorale: | ED 432 ECOLE DOCTORALE SCIENCES DES METIERS DE L'INGENIEUR |
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| Discipline: | Mécanique |
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| Collection (Fonds): | ENSAM |
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| Institution: | ENSAM |
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| Subjects: | 5. Fluid Mechanics and Energy |
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| Uncontrolled Keywords: | Matrix-Free implicit treatment, low-Mach preconditioning, steady-unsteady low-Mach number flows, Von Neumann analysis, PJ and SGS relaxation procedures, Unstructured grids, CPU time efficiency, Low memory requirements, Méthode implicite sans matrice, préconditionnement bas-Mach, écoulements stationnaires et instationnaires à faible nombre de Mach, analyse de Von Neumann, relaxation PJ et SGS, Maillages non-structurés, efficacité en temps CPU, Faible encombrement mémoire |
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