Micro-macro Methods for the Multiscale Simulation of Viscoelastic Flow Using Molecular Models of Kinetic Theory

We survey the field of micro-macro numerical techniques for predicting complex flows of viscoelastic fluids. The micro-macro approach couples the mesoscopic scale of kinetic theory to the macroscopic scale of continuum mechanics. A numerical solution is sought to the coupled non-linear problem involving the conservation laws and a microstructural model of kinetic theory. Although micro-macro techniques are much more demanding in terms of computer resources than conventional continuum computations, they allow the direct use of kinetic theory models in flow simulations, thus avoiding potentially inaccurate closure approximations. The focus of our survey is mainly put on mathematical formulations and numerical approaches. Applications to polymer solutions and melts, liquid crystalline polymers, and fibre suspensions, are briefly reviewed.