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Modèles multi-échelles pour les fluides viscoélastiques

Abstract : The most important part of this work deals with the mathematical analysis of multiscale models of polymeric fluids. These models couple, at the microscopic level, a molecular description of the evolution of the polymer chains (in terms of stochastic differential equations) and, at the macroscopic level, the mass
conservation and momentum equations for the solvent (which are partial differential equations). In Chapter 1, we introduce the models and give the main results obtained. In Chapters 2, 4, 5 and 7 we make precise the mathematical meaning and the well-posedness of the equations in either homogeneous flows or plane shear flows for some specific models of polymer chains. In Chapters 2, 3, 6 and 7, we analyse and prove convergence of some numerical schemes. Finally, in Chapter 8, we deal with the longtime behaviour of the coupled system. A second part of this document concerns a magnetohydrodynamic (MHD) problem coming from industry. In Chapter 9, we introduce the problem and the numerical methods used. We present a new test-case in MHD in Chapter 10. Finally, we give a stability analysis of the scheme in Chapter 11.
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Contributor : Tony Lelièvre <>
Submitted on : Thursday, September 2, 2004 - 4:23:40 PM
Last modification on : Friday, November 29, 2019 - 12:42:01 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:07:23 PM


  • HAL Id : tel-00006797, version 1



Tony Lelièvre. Modèles multi-échelles pour les fluides viscoélastiques. Modélisation et simulation. Ecole des Ponts ParisTech, 2004. Français. ⟨tel-00006797⟩



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