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Modélisation, étude mathématique et simulation des collisions

Abstract : This thesis deals with the study of complex fluids in Fluid Mechanics, and particularly of sprays (i.e. particles in suspension in a surrounding fluid).The physical quantities are solutions of partial differential equations (PDE). The continuous phase (surrounding fluid) is described by Euler or Navier-Stokes type equations. The dispersed phase is described by a kinetic equation.

The first part is devoted to a mathematical study of a coupling between a Vlasov equation, and the isentropic Euler equations, which appears in the modelling of thin sprays. We establish the existence for small time of a regular solution for the Vlasov-isentropic Euler system.

Next, we write down the precise kernels corresponding to the complex phenomena of oscillations, breakup and collisions/coalescences.

Then, we describe the numerical simulation of a kinetic-fluid coupling in an industrial code (Commissariat à l'Énergie atomique); we especially study the implementation of collisions in the code.

A second model of breakup is also presented. This model is more adapted when droplets interact with a pressure wave and have an high Weber number.

Finally, we give explicit estimates for the spectral gap of the linearized Boltzmann and Landau operators with hard potentials.
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Contributor : Céline Baranger <>
Submitted on : Sunday, March 20, 2005 - 6:51:25 PM
Last modification on : Thursday, April 15, 2021 - 3:31:52 AM
Long-term archiving on: : Friday, April 2, 2010 - 10:07:06 PM


  • HAL Id : tel-00008826, version 1


Céline Baranger. Modélisation, étude mathématique et simulation des collisions. Mathématiques [math]. École normale supérieure de Cachan - ENS Cachan, 2004. Français. ⟨tel-00008826⟩



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