# Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats

## TL;DR

This paper examines the challenges of molecular dynamics in hybrid multiscale methods, offering insights on simulation strategies, thermostat choices, finite-size effects, and proposing a new reduced-order coupling technique to improve efficiency.

## Contribution

It provides a detailed analysis of molecular simulation pitfalls in HMM and introduces a novel reduced-order method for coupling microscopic and macroscopic models.

## Key findings

- Simulating many small systems is preferable to few large ones.
- Simple isokinetic thermostats are generally sufficient.
- The proposed reduced-order technique efficiently approximates non-linear stress-strain relations.

## Abstract

Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation boxes. We also argue that if colloidal systems are considered as opposed to atomistic systems, the gap between microscopic and macroscopic simulations regarding time and length scales is significantly smaller. We also propose a novel reduced-order technique for the coupling to the macroscopic solver, which allows us to approximate a non-linear stress-strain relation efficiently and thus further reduce computational effort of microscopic simulations.