Modélisation numérique d'écoulements fluide/particules

Abstract : This PhD thesis is made of three parts.
In the first one, we present a method to simulate fluid/particle flows. We show that the penalty method, combined to a time discretization performed using the method of characteristics leads to a generalized Stokes variational formulation. Numerical tests are implemented with FreeFem++ to study the convergence. We also present three examples using this method.
In the second part we propose a model to take into account lubrication forces in direct simulations of fluid/particle flows. We first present a "viscous contact" model in the plane/particle case, obtained as the vanishing viscosity limit of the lubrication model. Then, we describe an algorithm based on a projection of the velocities, at each time step, over a set of admissible velocities. Next, we prove the convergence of the scheme and generalize the algorithm to the multi-particle case. We also present an example of object oriented programming of it.
In the last part, we consider a discrete system of spheres (chain in 1D) interacting through a lubrication force. The microscopic model relies on the development of that force at small distance. We propose a macroscopic constitutive equation, of Newtonian type, which relies on an elongational viscosity which is proportional to the reciprocal of the local fluid fraction. We establish the convergence of the microscopic model towards the solution of the proposed macroscopic model.
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Theses
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https://tel.archives-ouvertes.fr/tel-00257246
Contributor : Aline Lefebvre-Lepot <>
Submitted on : Monday, February 18, 2008 - 6:35:27 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Long-term archiving on : Thursday, May 20, 2010 - 7:07:45 PM

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Aline Lefebvre, Aline Lefebvre-Lepot. Modélisation numérique d'écoulements fluide/particules. Mathématiques [math]. Université Paris Sud - Paris XI, 2007. Français. ⟨tel-00257246⟩

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