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Divers problèmes théoriques et numériques liés à la simulation de fluides non newtoniens

Abstract : This thesis is devoted to the modelling, the mathematical analysis and the simulation of non-Newtonian fluids. Some fluids in an intermediate liquid-solid phase are particularly considered: aging fluids. Modelling scales are macroscopic and mesoscopic. In Chapter 1, we introduce the models and give the main results obtained. In Chapter 2, we present numerical simulations of a macroscopic two-dimensional model. The finite element method used for discretization is described. For the flow past a cylinder test-case, phenomena at play in aging fluids are observed. The Chapter 3 contains a mathematical analysis of the one-dimensional version of the system of partial differential equations used for the simulations. We show well-posedness and investigate the longtime behaviour of the solution. In the last chapter, macroscopic equations are derived from a mesoscopic equation. The mathematical analysis of this mesoscopic equation is also carried out
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Submitted on : Tuesday, June 3, 2014 - 3:47:28 PM
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  • HAL Id : tel-00973407, version 2



David Benoit. Divers problèmes théoriques et numériques liés à la simulation de fluides non newtoniens. Mathématiques générales [math.GM]. Université Paris-Est, 2014. Français. ⟨NNT : 2014PEST1004⟩. ⟨tel-00973407v2⟩



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