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Mathematical analysis and numerical simulations of a model of complex fluids

Yousra Gati
Abstract : We are interested in the mathematical analysis and numerical simulations of a model of non Newtonian fluids. We couple the Hébraud-Lequeux model that describes the planar Couette flow of concentrated suspensions with the momentum conservation equation. Besides the coupling of equations, the principal difficulty of the model comes from the fact that the microscopic equation is a non-linear parabolic equation of Fokker-Planck type that may degenerate into a hyperbolic equation. The purpose of this work is to study this model from both theoretical and numerical viewpoints. In the first part, we prove existence and uniqueness of solutions in a appropriate functional spaces. In the second one, we develop numerical schemes to simulate the model. Two methods (deterministic and stochastic) have been implemented. Variance reduction techniques have been developed to reduce the noise when the stochastic method is employed. Finally, optimisation techniques are used to fit the parameters of the model.
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https://pastel.archives-ouvertes.fr/pastel-00000883
Contributor : Ecole Des Ponts Paristech <>
Submitted on : Thursday, November 4, 2004 - 8:00:00 AM
Last modification on : Thursday, November 4, 2004 - 8:00:00 AM
Long-term archiving on: : Thursday, September 30, 2010 - 5:58:00 PM

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  • HAL Id : pastel-00000883, version 1

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Yousra Gati. Mathematical analysis and numerical simulations of a model of complex fluids. domain_other. Ecole des Ponts ParisTech, 2004. English. ⟨pastel-00000883⟩

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