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Carnegie Mellon Center for Nonlinear Analysis
A Mathematical Viewpoint on Multiscale Models for Polymeric Fluids


Tony Lelièvre
École des Ponts ParisTech

: We will first present some multiscale (or micro-macro) models which have been introduced to describe the behaviour of polymerics fluids. These models rely on the coupling of classical momentum and mass conservation equations at the macroscopic level, with kinetic equations to model the evolution of the polymers within the fluid, that yield the stress through ensemble averages. After a short discussion of the modelling approach, we will present two mathematical aspects: (i) the long-time behaviour for such models and the derivation of free-energy dissipative finite element schemes and (ii) some numerical approaches to obtained closed evolution on the stress, starting from a micro-macro model.

pdf of talk , link to review article