Enhancements to the Meso Scale Model - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 111

0.2

0

0 50 100 150 200 250 350

300 400

− 0.2

− 0.4

− 0.6

− 0.8

1

−

− 1.2

Number of time steps in sample

Figure 4.5 Graph showing the average value of velocity plotted against the number of
time steps between samples.

contains a significant level of noise making a relationship difficult to determine,
but the average velocity shows a definite trend to zero as the sample time in-
creases, giving a very close approximation for sample times greater than 250 time
steps.
Both of these graphs demonstrate the same result. The more time molecules
are allowed in order to change state before being re-sampled, the better the
interrogation of the available phase space performed by each of the local
approximations. In both cases, the improvement is exponential, although the aver-
age velocity data are noisy. However, a longer time between samples reduces the
resolution of the ensembles in terms of simulation time. This must be considered
when long sample times are used. A way of increasing the time between samples
is to take fewer samples per ensemble, which will be discussed in detail in the
next case study:

4.4.1.2 Case Study 2: number of samples per ensemble

By performing a similar study, the effect of the number of samples collected
per ensemble average can be investigated. Simulations were set up as described
above, with the samples taken at regular intervals of 75 time steps, but the ensem-
bles were constructed with between 2 and 40 samples.