The Nature of Fluid Flow - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 25

Additional information on the Monte Carlo simulation method and its different
ensembles can be found in the topic by Gould et al. [17]. Gould provides examples
of Monte Carlo methods, focusing on its advantages at simulating phase changes,
which has been used to good effect by Levesque et al. [18] applied to hydrogen
storage in carbon nanotubes.
1.4.2 Molecular Dynamics
Molecular dynamic (MD) simulations model fluid in two ways, with molecules
being represented as hard or soft spheres. Modelling with hard sphere models
provides a relatively simple approach to approximating a system of molecules but
still has valid applications, such as looking into the liquid-gas phase transition
and diffusion, and hard sphere fluids have a well-defined critical point. The draw-
backs are mainly to do with the discontinuous nature of the model. The collisions
are performed instantaneously and spheres only interact repulsively, whereas real
systems have some form of attraction between particles. Because of this, it is also
used for gas simulations where the distances between molecules are far greater
than their diameter, and intermolecular interactions occur rarely. Despite these
disadvantages, the model is still widely and successfully used, but care must be
taken to ensure that it is appropriate to the situation being simulated.
A more realistic, but more complex and computationally demanding approach,
is the soft sphere model. In this model, the long-range attractive and repulsive
forces are modelled as a continuous function of the separation between pairs of
molecules. The use of a continuous interaction function improves the accuracy of
the simulation at the cost of increasing the computational load.
1.4.3 Introduction to the Physics of MD Simulations
Molecular dynamic simulations work on the same basic principles regardless of
the actual interaction laws (hard or soft spheres) and rely on the following three
steps: initialization, equilibrium and production. These stages are detailed below
following the example of a molecular scale cubic cell suspended in a fluid away
from any physical boundaries, as shown in Figure 1.12.
1.4.3.1 Initialization
When the simulation is run, the first task performed is to define the problem; this
is known as initialization. This stage of the simulation accounts for only one time
step and is used to create the system of spheres based on a set of user-defined
parameters. In the example used, a control volume suspended in a fluid of set
volume and density is simulated (Figure 1.12). The initialization stage is where