Lagrangian Heterogeneous Multiscale Method (LHMM) for Simulating Polymer Solutions/Melts Behavior under Complex Flows using DPD-SPH
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| Format: | Preprint |
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2025
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| author | Patiño-Nariño, Edgar A. Moreno, Nicolas Ellero, Marco |
| author_facet | Patiño-Nariño, Edgar A. Moreno, Nicolas Ellero, Marco |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lagrangian Heterogeneous Multiscale Method (LHMM) for Simulating Polymer Solutions/Melts Behavior under Complex Flows using DPD-SPH Patiño-Nariño, Edgar A. Moreno, Nicolas Ellero, Marco Fluid Dynamics Applied Physics 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. |
| title | Lagrangian Heterogeneous Multiscale Method (LHMM) for Simulating Polymer Solutions/Melts Behavior under Complex Flows using DPD-SPH |
| topic | Fluid Dynamics Applied Physics |
| url | https://arxiv.org/abs/2512.13267 |