A numerical closure approach for kinetic models of polymeric fluids: exploring closure relations for FENE dumbbells

TL;DR

This paper introduces a numerical method to evaluate closure approximations for FENE dumbbells in polymeric fluids, helping identify effective macroscopic variables for accurate modeling.

Contribution

It presents a novel numerical procedure to test and compare closure relations based on macroscopic variables for FENE dumbbells in polymeric fluid models.

Findings

Closure relations are related to quasi-equilibrium approximations.

The method effectively tests different sets of macroscopic variables.

Numerical results guide the selection of variables for better closures.

Abstract

We propose a numerical procedure to study closure approximations for FENE dumbbells in terms of chosen macroscopic state variables, enabling to test straightforwardly which macroscopic state variables should be included to build good closures. The method involves the reconstruction of a polymer distribution related to the conditional equilibrium of a microscopic Monte Carlo simulation, conditioned upon the desired macroscopic state. We describe the procedure in detail, give numerical results for several strategies to define the set of macroscopic state variables, and show that the resulting closures are related to those obtained by a so-called quasi-equilibrium approximation \cite{Ilg:2002p10825}.