École des Ponts ParisTech
lelievre@cermics.enpc.fr
Abstract: 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.