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Calcul d'écoulements extérieurs incompressibles

Abstract : We aim to approach the solution of stationary incompressible Navier-Stokes systems in a three-dimensional exterior domain. So, we impose some appropriate conditions to the free boundary of the computational domain.
We discretize by equal order finite elements with stabilization, thus the linearisation leads to a generalized saddle point problem. We choose to solve the complete system by a Krylov method. The remaining difficulties are the preconditioning of two matrices:
the Schur complement matrix and the convection-diffusion matrix.

At first, we prove that the mass matrix is spectrally equivalent to the Schur complement, which means that our iteration count is independent of the size of the discretization space. We study theoretically the spectrum of the preconditioned problem with respect to the Reynolds number when the test-case is the driven cavity.
Next, we additionally analyze the dependence on the truncation radius for the exterior problem. The numerical three-dimensional results well confirm the theory and show the method robustness.

Afterwards, we propose a non-overlapping domain decomposition method for the convection-diffusion problem where the continuity of the solution is imposed by Lagrange multipliers. We study the performance of a preconditioner for the interface problem, so that we extend to the three-dimensional case some two-dimensional numerical results of the literature.

An other part of this document, independent of the thesis subject, is devoted
to a work concerning plasma physics realized during CEMRACS 2003.
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Contributor : Delphine Jennequin <>
Submitted on : Thursday, March 9, 2006 - 3:58:02 PM
Last modification on : Sunday, November 29, 2020 - 3:24:04 AM
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  • HAL Id : tel-00011893, version 1



Delphine Jennequin. Calcul d'écoulements extérieurs incompressibles. Mathématiques [math]. Université du Littoral Côte d'Opale, 2005. Français. ⟨tel-00011893⟩



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