Combined micro--macro integration scheme from an invariance principle: application to ferrofluid dynamics

TL;DR

This paper introduces a combined micro-macro simulation method based on invariance principles, applied to ferrofluid dynamics, which adaptively switches between microscopic and macroscopic models for improved accuracy.

Contribution

The paper presents a novel invariance-based scheme that dynamically integrates microscopic and macroscopic simulations, enhancing modeling flexibility in ferrofluid dynamics.

Findings

Successfully switches between Brownian dynamics and constitutive equation integration

Demonstrates improved accuracy in ferrofluid flow simulations

Validates the invariance principle for adaptive multiscale modeling

Abstract

A method for the combination of microscopic and macroscopic simulations is developed which is based on the invariance of the macroscopic relative to the microscopic dynamics. The method recognizes the onset and breakdown of the macroscopic description during the integration. We apply this method to the case of ferrofluid dynamics, where it switches between direct Brownian dynamics simulations and integration of the constitutive equation.