Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics

Tins paper is an introduction to the modelling of viscoelastic fluids, with an emphasis on micro-macro (or multiscale) models. Some elements of mathematical and numerical analysis are provided. These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop Stress Tensor Effects on Fluid Mechanics in January 2010.