Environmental Engineering Reference
In-Depth Information
larly a calculation, which requires memory, which far exceeds that, which is avail-
able, can be carried out only by using very sophisticated programming techniques,
which slow down running speeds and greatly increase the probability of errors. It
is therefore important that the user first consider the requirements of both memory
and CPU time before embarking on a project to ascertain whether or not there is a
realistic possibility of obtaining the resources to SIM [136].
1.3.1.2.2
STATISTICAL AND OTHER ERRORS
Assuming that the project can be done, there are still potential sources of error,
which must be considered. These difficulties will arise in many different situations
with different algorithms so we wish to mention them briefly at this time without
reference to any specific simulation approach. All computers operate with limited
word length and hence limited precision for numerical values of any variable.
Truncation and round-off errors may in some cases lead to serious problems. In
addition there are statistical errors, which mention before. What difficulties will
we encounter? An inherent feature of the simulation algorithm due to the finite
number of members in the 'statistical sample,' which is generated. These errors
must be estimated and then a 'policy' decision must be made, that is, should more
CPU time be used to reduce the statistical errors or should the CPU time available.
1.3.1.2.3 WHAT STRATEGY SHOULD FOLLOWED IN APPROACHING
A PROBLEM?
Most new simulations face hidden pitfalls and difficulties, which may not be ap-
parent in early phases of the work. It is therefore often advisable to begin with
a relatively simple program and use relatively small system sizes and modest
running times. Sometimes there are special values of parameters for which the
answers are already known (either from analytic solutions or from previous, high
quality simulations) and these cases can be used to test a new simulation program.
By proceeding in this manner one is able to uncover which are the parameter
ranges of interest and what unexpected difficulties are present. It is then possible
to refine the program and then to increase running times. Thus bothCPU time and
human time can be used most.
1.3.1.2.4 HOW DO SIMULATIONS RELATE TO THEORY AND
EXPERIMENTAL WORKS?
In many cases theoretical treatments are available for models for which there
is no perfect physical realization (at least at the present time). In this situation
the only possible test for an approximate theoretical solution is to compare with
'data' generated from a computer simulation. As an example we wish to mention
recent activity in growth models, such as diffusion-limited aggregation, for which
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