From Micro to Macro Dynamics via a New Closure Approximation to the FENE Model of Polymeric Fluids

We present a new closure approximation needed for deriving effective macroscopic moment equations from the microscopic finite-extensible-nonlinear-elastic kinetic theory modeling viscoelastic polymeric fluids. The closure is based on restricting the otherwise general probability distribution functions (PDFs) to a class of smooth distributions motivated by perturbing the equilibrium PDF\@. The simplified system coupling the moment equations and the Navier--Stokes equations still possesses an energy law analogous to the original micro-macro system. Some theoretical analysis and numerical experiments are presented to ensure the validity of the moment-closure system, and to illustrate the excellent agreement of the simplified model with the original system solved using a Monte Carlo approach, for a certain regime of physical parameters.