Multiscale flow simulations of dilute polymeric solutions with bead-rod chains using Brownian configuration fields

Abstract

We couple the momentum and mass balance equations with the bead-rod chain model (Kramers chain) to simulate non-Newtonian polymeric fluids using finite elements and the Brownian configuration field method. A suitable rod-length preserving discretization is presented, which is based on the ideas of Liu's algorithm [28] and generalized into the finite-element context. Additional details concerning the parallelization of the Brownian configuration field part of the simulation are discussed to achieve outstanding code runtimes on large computation clusters. The novel coupling enables the investigation of how the bead-rod chains influence the fluid flow. This is done with proof-of-concept simulations for the start-up shear flow and flow around a cylinder scenario in 2D that serve as a reference for future research. In the start-up shear flow scenario, the velocity overshoot effect, which is typical for polymeric fluids, is successfully demonstrated. In the more challenging flow around a cylinder scenario, we numerically confirm the viscoelastic drag reduction phenomenon by comparing the drag coefficients with a purely Newtonian Navier–Stokes solution.