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Analyse et mise en oeuvre de nouveaux algorithmes en méthodes spectrales

Abstract : This thesis is composed of three parts. In the first part, we consider the 3D Reynolds Averaged Navier-Stokes model, coupling two turbulent fluids (for instance ocean/atmosphere). We propose a numerical schem and we show its convergence to the unique solution of the model.
The second part is devoted to an extension of spectral methods in complex geometries. This method is based an twi ideas: following Nitsche'method, the use of penalization method for Dirichlet boundary conditions, and an approximation of the geometry by pavements using octree(for instance).
We give polynomial errors projection and a priori estimates.
Finally, we have developed in C++ and validated the method in the FreeFem3d software.
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Contributor : Driss Yakoubi <>
Submitted on : Friday, February 13, 2009 - 7:29:09 PM
Last modification on : Wednesday, December 9, 2020 - 3:13:11 PM
Long-term archiving on: : Friday, October 12, 2012 - 11:45:55 AM


  • HAL Id : tel-00361368, version 1


Driss Yakoubi. Analyse et mise en oeuvre de nouveaux algorithmes en méthodes spectrales. Modélisation et simulation. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00361368⟩



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