An Enhanced Macroscopic Closure Approximation to the Micro-Macro FENE Model for Polymeric Materials

Abstract

We present an enhanced moment-closure approximation to the finite extensible nonlinear elastic (FENE) models of polymeric fluids. This new moment-closure method involves the perturbation of the equilibrium probability distribution function (PDF), which takes into account of the drastic split into two spikes and centralized behavior under the large macroscopic flow effects. The resulting macroscopic system includes the moment-closure equations, the momentum (force balance) equations, as well as an auxiliary equation representing implicitly the dynamics of the spikes for the microscopic configurations. It also inherits the energy dissipation law from the original micro-macro models. Through numerical experiments, we demonstrate the accuracy and robustness of the moment-closure system for some special external flow with a wide range of flow rates.