On the coupling of molecular dynamics to continuum computational fluid dynamics

Abstract

Molecular dynamics (MD) is a discrete modelling technique that is used to capture the nanoscale motion of molecules. MD can be used to accurately simulate a range of physical problems where the continuum assumption breaks down. Examples include surface interaction, complex molecules, local phase changes, shock waves or the contact line between fluids. However, beyond very small systems and timescales (μm and msec), MD is prohibitively expensive. Continuum computational fluid dynamics (CFD), on the other hand, is easily capable of simulating scales of engineering interest, (m and s). However, CFD is unable to capture micro-scale effects vital for many modern engineering fields, such as nanofluidics, tribology, nano-electronics and integrated circuit development. This work details the development of a set of techniques that combine the advantages of both continuum and molecular modelling methodologies, allowing the study of cases beyond the range of either technique alone. The present work is split into both computational and theoretical developments. The computational aspect involves the development of a new high-performance MD code, as well as a coupler (CPL) library to link it to a continuum solver. The MD code is fully verified, has similar performance to existing MD software and allows simulation of a wide range of cases. The CPL library is a robust, flexible and language independent API and the source code has been made freely available under the GNU GPL v3 license. Both MD and CPL codes are developed to allow very large scale simulation on high performance computing (HPC) facilities. The theoretical aspect includes the development of a rigorous mathematical framework and its application to develop novel coupling methodologies. The mathematical framework allows a discrete molecular system to be expressed in terms of the control volume (CV) formulation from continuum fluid dynamics. A discrete form of Reynolds’ transport theorem, is thus obtained, allowing both molecular and continuum systems to be expressed in a consistent manner. This results in a number of important insights into the molecular definition of stress. This CV framework allows mathematical operations to be localised to a control volume in space. It is ideally suited to apply coupling constraints to a region in space. To link the CFD and MD solvers in a rigorous and physically consistent manner, the CV framework is combined with the variational principles of classical mechanics. The result is a unification of a number of existing forms used in the coupling literature and a rigorous derivation of a new and more general coupling scheme.