Molecular dynamics (MD) is a discrete modelling technique that is used to capture the nano-
scale 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 com-
putational 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 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 equations used in the
coupling literature and a rigorous derivation of a new and more general coupling scheme.