# A hybrid particle-continuum method for hydrodynamics of complex fluids

## TL;DR

This paper extends a hybrid particle-continuum method to dense fluids and multi-dimensional flows, demonstrating its ability to accurately reproduce microscopic dynamics and non-equilibrium phenomena by incorporating thermal fluctuations into the continuum solver.

## Contribution

The paper generalizes a hybrid particle-continuum scheme to dense fluids and higher dimensions, emphasizing the importance of including fluctuations in continuum solvers for accurate multiscale modeling.

## Key findings

- Hybrid method accurately reproduces bead velocity autocorrelation.
- Including fluctuations in the continuum solver is essential.
- Correctly models non-equilibrium relaxation of the adiabatic piston.

## Abstract

A previously-developed hybrid particle-continuum method [J. B. Bell, A. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6:1256-1280, 2008] is generalized to dense fluids and two and three dimensional flows. The scheme couples an explicit fluctuating compressible Navier-Stokes solver with the Isotropic Direct Simulation Monte Carlo (DSMC) particle method [A. Donev and A. L. Garcia and B. J. Alder, ArXiv preprint 0908.0510]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary conditions for the continuum subdomain. The equilibrium diffusive (Brownian) motion of a large spherical bead suspended in a particle fluid is examined, demonstrating that the hybrid method correctly reproduces the velocity autocorrelation function of the bead but only if thermal fluctuations are included in the continuum solver. Finally, the hybrid is applied to the well-known adiabatic piston problem and it is found that the hybrid correctly reproduces the slow non-equilibrium relaxation of the piston toward thermodynamic equilibrium but, again, only the continuum solver includes stochastic (white-noise) flux terms. These examples clearly demonstrate the need to include fluctuations in continuum solvers employed in hybrid multiscale methods.