Continuum-particle hybrid coupling for mass, momentum and energy transfers in unsteady fluid flow

TL;DR

This paper presents a hybrid simulation method coupling atomistic and continuum fluid dynamics to accurately model unsteady flows with energy exchange, validated through various flow scenarios and energy considerations.

Contribution

It introduces a two-way coupling scheme for unsteady flows that effectively handles energy transfer between atomistic and continuum regions.

Findings

The scheme accurately reproduces hydrodynamic trends in flow variables.

It preserves the correct rate of entropy production.

Effective for both steady and unsteady flow scenarios.

Abstract

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C->P and P->C) which conveys mass, momentum and energy fluxes. The contribution of the hybrid scheme hereby presented is two-fold: first it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.