The
Big Picture
What
have we been doing? Computer simulation is
a method of performing
experiments without costly hardware. To
be in this business, you need to become a very good experimentalist. Always remember that your experiments are
performed in virtual worlds where the physical laws may be close to
those of
the real world, but never really match.
You’ve got to use your full training as an engineer to detect
the
differences in physical laws and understand their impact.
Never trust the results of a computer
simulation until you (or someone you know and trust) have thoroughly
tested the
relationship between the virtual and real worlds.
If
you haven’t learned the skills
already, spend time learning how to construct controlled experiments. One major advantage of computer simulations
is that you have far more opportunities for highly controlled
experiments than
you do in the real world. During this
process you will be applying basic scientific method:
1.
Make careful observations
of a system;
2.
Make a hypothesis to
explain those observations;
3.
Design a test (or tests)
for the hypothesis;
4.
Perform the test;
5.
Either confirm your
hypothesis, or revise it (loop back to 2).
When
designing a test, limit the
changes you introduce into the system.
In computer simulation, there is almost never an excuse for
introducing
more than one change at a time.
While
we’re talking about
science, I want to introduce a broader definition.
One of our basic characteristics as human beings
is that we see what we want to see. This
is not wholly a weakness. Science is a
discipline that we have built over millennia, to help us see what is
really
there. When properly used Computer
Simulation is a tool that can help us see what is really there. However, be cautious of your fundamental
nature. Do not except the results of a
computer simulation (or any other observation) because they are what
you want
to see. Use all of your experience and
training to be certain that the results adequately reflect reality.
1.
Determine appropriate
mathematical model
2.
Classification of partial
differential equation
3.
Transformation of
mathematical model
4.
Select grid pattern
5.
Formation of finite
difference equations
6.
Solution algorithm
7. Perform auxiliary calculations
Topics for the Second Exam |
More Stability Analysis
(von Neumann, Hirt’s method) |
A
sample testbed
program |
Wiggles |
Application
to Multi-phase and/or reacting flow |