Navier-Stokes Equations & CA & AutoCAD

[mailrus!jarvis.csri.toronto.edu!utgpu!watmath!watdragon!dahlia!sasingh@xxxxxxxxxxxxxxx (Sanjay Singh)]

I have just pulled Cellular Automata Machines out of the library, and
see an opportunity to challenge a friend who works with finite elements
for compressible fluid flow. I don't feel that the FEM is quite right
in that it assumes a continuum and proceeds to discretize it. I like the
idea of CA better.

Firstly, if someone is familiar with the Toffoli and Margolus book, or
citations from it to Wolfram's Theory and Applications of CA, regarding
approximations of fluid flow, please get back to me, with some sort of
psuedo-code that embodies the cellular-automaton laws. 

Once I have the laws for imcompressible flow down pat, the other problem
would be to alter the laws to model compressible flow, since that is what
airflow is all about. Air can be compressed, water cannot. So it would seem
that a simulation of incompressible flow, which is what is documented in the
book, cannot model such phenomenon as a sonic boom, or air patterns at
Mach 3. Since I am primarily interested in optimizing bicycle frames, these
perhaps could be safely neglected.

I would like to proceed from the design phase to the testing phase as smoothly
as possible. So to understand how AutoCAD stores its drawings would be a
benefit. Software does exist that can take an AutoCAD drawing and proceed
to do furthur work. Could anyone kindly refer me to third-party publications
which would explain this furthur?

The final problem involves the computation of drag. Indeed, how _does_ one
actually abstract the results of millions of particles hitting an object
into a nice, neat drag coefficient. No books on CA thus far elaborate on
this. Perhaps the notion of fractal dimension could be invoked, whereby,
the more a particle deviates from a straight line, the higher the fractal
dimension of the path of the particle in space, and the more energy
required to make the particle move in a straight line. 

Anyhow, thanks for your consideration in reading this. Any assistance
would be greatly appreciated.

Sanjay A Singh.
sasingh@xxxxxxxxxxxxxxxxxxx