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Méthode de la frontière élargie pour la résolution de problèmes elliptiques dans des domaines perforés. Application aux écoulements fluides tridimensionnels

Abstract : The aim of this thesis is the mathematical analysis of the Fat Boundary Method (F.B.M.) and its adaptation to the numerical simulation of the 3D incompressible fluid flows in complex geometries (perforated domains). First, we focus on a simple case of model elliptic problems (Poisson or Helmholtz-like problems) set in a perforated domain (typically a box containing spherical obstacles). Using F.B.M., the initial problem is replaced by a new one defined in the entire box, making it possible to use a cartesian grid, thus offering a suitable framework for the use of fast solvers. We thus carry out the mathematical analysis of the F.B.M., in particular the convergence and the errors estimate. The obtained theoretical results are also illustrated numerically. The second part is dedicated to the application of these tools for the Numerical Simulation of three-dimensional incompressible fluid flows. The strategy consists in discretizing the Navier-Stokes equations by combining the F.B.M. (for the space discretization), a Projection Scheme (for the time discretization) and the Characteristics Method (for the treatment of the convection). Finally, we present several three-dimensional Numerical Simulations corresponding to fluid flows in presence of fixed and mobile obstacles (imposed motion).
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https://tel.archives-ouvertes.fr/tel-00006401
Contributor : Mourad Ismail <>
Submitted on : Wednesday, July 7, 2004 - 3:01:44 PM
Last modification on : Friday, May 29, 2020 - 4:01:22 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:15:48 PM

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  • HAL Id : tel-00006401, version 1

Citation

Mourad Ismail. Méthode de la frontière élargie pour la résolution de problèmes elliptiques dans des domaines perforés. Application aux écoulements fluides tridimensionnels. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. Français. ⟨tel-00006401⟩

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