Particle–Continuum Coupling and its Scaling Regimes: Theory and Applications

Abstract

This work is motivated by the goal of designing simulation software for technical devices that, at their functional core, rely on atomistic-scale processes embedded in a larger-scale fluid environment. The core of the problem is the conceptual and technical approach for coupling particle and continuum representations of a fluid. The state of the art for key aspects including physical modeling, mathematical formalization, computational implementation, and applications, is discussed and organized in a consistent picture across the relevant physical regimes.Key building blocks of the related developments that we will summarize and appraise in some detail below are i) finite volume FHD solvers following Bell, Donev, Garcia, Nonaka and colleagues [4] (see Section 2), ii) the "adaptive resolution simulation" (AdResS) approach that enables molecular dynamics simulations on limited size domains [5][6][7] (see Section 3), and iii) the recent mathematical formalization of open molecular systems by two of the authors [8] (see Section 4). In Section 5, we discuss scaling regimes and the rationale behind possible MD-FHD coupling strategies, finally, Section 6 is dedicated to the description of some representative examples, while Section 7 outlines future perspectives and summarizes our conclusions.

From adaptive resolution to molecular dynamics of open systems

“…In this paper, being focused more on the computational aspects, the mathematical analysis will not be discussed in detail, nevertheless it is worth to underline the multidisciplinary character of AdResS. In fact its numerical results have stimulated the formalization of new equations for open particle systems under different conditions [34,36] which in turn, in perspective, can be automatically embedded in the equations of fluid dynamics [37].…”

A Thermostat‐Consistent Fully Coupled Molecular Dynamics—Generalized Fluctuating Hydrodynamics Model

“…The modified MD particle equations are solved by the standard Leapfrog algorithm [31] and using appropriate central finitevolume approximation for the continuum forcing terms for the MD particle coordinate (18) and velocity…”

“…[ 16,17 ] Such refined formulations can be used to obtain sophisticated triple‐scale (micro–meso–macro) models where multiresolution particles are coupled with continuum flow models. [ 17,18 ]…”

“…[16,17] Such refined formulations can be used to obtain sophisticated triple-scale (micro-meso-macro) models where multiresolution particles are coupled with continuum flow models. [17,18] The current work follows the hybrid modeling approach developed in refs. [19] and [20] .…”

A Thermostat‐Consistent Fully Coupled Molecular Dynamics–Generalized Fluctuating Hydrodynamics Model for Non‐Equilibrium Flows

“…Consequently, the coarse-grained particles are coupled with the continuum flow models which lead to a micro-meso-macro scale formulation. [8,9] For multi-resolution fluid dynamics modeling, the coupling between the models of different resolutions should respect conservation of both the mass and the linear momentum. To automatically satisfy these conservation laws, the two-phase analogy multiscale method was suggested in, [10,11] which considered the continuum and atomistic representations of a liquid as phases of a nominally two-phase flow.…”