Hybrid Multiscale Method for Polymer Melts: Analysis and Simulations

ABSTRACT We model the flow behaviour of dense melts of flexible and semiflexible ring polymers in the presence of walls using a hybrid multiscale approach. Specifically, we perform molecular dynamics simulations and apply the Irving–Kirkwood formula to determine an averaged stress tensor for a macroscopic model. For the latter, we choose a Cahn–Hilliard–Navier–Stokes system with dynamic and no‐slip boundary conditions. We present numerical simulations of the macroscopic flow that are based on a finite element method. In particular, we present detailed proofs of the solvability and the energy stability of our numerical scheme. Phase segregation under flow between flexible and semiflexible rings, as observed in the microscopic simulations, can be replicated in the macroscopic model by introducing effective attractive forces.