Modélisation et simulations numériques pour des systèmes de la mécanique des fluides avec contraintes; application à la biologie et au trafic routier

Bastien Polizzi 1, 2
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : The works presented in this thesis are devoted to the study of partial differential equations systems (PDE). In particular, we are interested in constrained systems coming from the fluid mechanics field which allow to described, in time and space, physical quantities such as density or speed. In this context, we build models for biology which are then numerically tested. We also present an original numerical method for a road traffic model. In the first part, using the theory of mixtures, we model the development of a photosynthetic micro-algae biofilm. The growth of micro-algae is precisely described by taking into account their composition and their access to nutrients dissolved in the surrounding liquid and light. Then, using numerical simulations, we estimate the biofilm productivity. In the second part, using the mixture theory we propose a model describing the rheology of the large intestine and its mucus layer. Thanks to this model we can give an accurate description of the velocity field induced by intestinal flow. This velocity field will then be used to build a model describing precisely interactions between the intestinal microbiota, the gastric broth and the host. For these two models numerical schemes are proposed and allow a first validation of the models. The last part is devoted to developing an asymptotic preserving scheme for the constraint Aw-Rascle system for road traffic. We present an explicit-implicit method based on a splitting technique in order to approximate the solutions of Aw-Rascle system with constraint, while relaxing the stability condition (CFL).
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Submitted on : Tuesday, January 3, 2017 - 1:59:05 PM
Last modification on : Friday, February 8, 2019 - 8:40:02 AM
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Bastien Polizzi. Modélisation et simulations numériques pour des systèmes de la mécanique des fluides avec contraintes; application à la biologie et au trafic routier. Equations aux dérivées partielles [math.AP]. Université Nice Sophia Antipolis, 2016. Français. ⟨tel-01421823⟩

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