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450
400
350
t
=
180 ps
300
250
200
150
100
50
t
=
0
0
0
10
20
40
50
60
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30
Position (nm)
Figure 6.10
Bulk ensemble velocity profiles taken at 2 ps intervals. At
t
=
0 the fluid is
at rest.
The time step used was 2 fs and samples were taken every 100 time steps.
The ensemble averages were calculated over all nodes every 2000 time steps. The
parametric study also found that larger times between samples and ensembles
gave the best results, but for these simulations relatively short times were chosen
to capture the development of the steady state solution.
Figure 6.10 shows the development of the solution for the low-density system
containing 20 000 molecules. This graph clearly shows the system's progress to
develop a steady state solution from
t
0 where the velocity of the system is
zero, to the final equilibrium state after 90 000 time steps at
t
=
0,
the initial velocity increase between ensembles is large and the data contains a lot
of variation, but as the simulation progresses the change in velocity between suc-
cessive profiles reduces until the equilibrium state is reached. Once equilibrium
has been reached, the successive velocity profiles are almost identical and show
significantly less variation than at the start of the simulation, where diffusion is a
higher component of the resultant velocity of the molecules.
The above simulation was repeated for systems of the same volume contain-
ing 40 000, 60 000 and 100 000 to examine the effect that a density increase
has on large systems in terms of both the fluid behaviour and the performance
of the simulation. All simulations were performed with the same approximated
=
180 ps. At
t
=
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