Lagrangian Heterogeneous Multiscale Method (LHMM) for Simulating Polymer Solutions/Melts Behavior under Complex Flows using DPD-SPH

TL;DR

This paper introduces LHMM, a multiscale simulation framework coupling DPD and SPH to accurately model the complex rheology of polymer melts in diverse flow conditions, overcoming limitations of traditional methods.

Contribution

The novel LHMM framework integrates microscale DPD with macroscale SPH in a concurrent manner, enabling detailed multiscale simulation of polymer rheology under complex flows.

Findings

Successfully captures shear-thinning and viscoelastic properties.

Validates against benchmark flows with consistent results.

Demonstrates applicability to heterogeneous porous media.

Abstract

We present a Lagrangian Heterogeneous Multiscale Method (LHMM) for simulating the non-Newtonian rheology of polymer melts in complex two-dimensional flows. The method couples Dissipative Particle Dynamics (DPD) at the microscale with a GENERIC-compliant Smoothed Particle Hydrodynamics (SPH) at the macroscale, in a concurrent framework, overcoming the limitations of traditional Eulerian-based methods in capturing long-memory and history-dependent effects. At the microscale, DPD serves as a virtual rheometer, employing FENE (Finitely Extensible Nonlinear Elastic) bead-spring polymer chains. This approach provides key rheological properties, including shear-thinning and zero-shear-rate viscosities, relaxation times, and viscoelastic dynamics, which are quantified via Carreau-Yasuda fitting and spectral analysis. The LHMM couples SPH-derived strain rates with microscopic stress responses using the Irving-Kirkwood formalism. This approach enables a concurrent interaction between macroscopic strain rates and microscopic stress tensors, ensuring a consistent viscoelastic response across scales. The method is validated against benchmark flows, including Reverse Poiseuille Flow and flow through a Periodic Array of Cylinders, across Weissenberg numbers $0.5 < \text{Wi} < 30$ and low Reynolds numbers ($\text{Re} < 1$). A final demonstration of flow in a 2D porous medium highlights LHMM's capability to handle highly heterogeneous geometries. The LHMM is implemented in LAMMPS, making it suitable for integrating multiple models to describe microscales. In contrast, large-scale simulations efficiently utilize GPU and CPU resources, managing multiple coupling and time-scaling levels to maintain numerical stability and accuracy. The framework offers a predictive, constitutive-free tool that links microscopic polymer dynamics to macroscopic flow behavior, making it suitable for multiscale applications.