i just read an interesting article in the current issue of Scientific
American about turbulence and supercomputers. as i read it, the topic of
computational geometry entered my mind. from memory, here's a brief gist
of the story:
the article discusses the work of researchers who have programmed the
world's best and fastest supercomputers to model the flow of fluids,
especially the flow of air (which is really a fluid) around airplanes.
with the computer simulations, engineers can refine their designs to cut
down on turbulence (e.g. the counterproductive formation of eddy
currents) which causes frictional drag forces. of course, more drag =
more fuel consumption = higher ticket prices.
the story has 5 or 6 paragraph explanation of what must be done in order
to run the computer simulation: the geometry of the plane (wings,
fuselage, nacelles, etc.) needs to be modelled, as well as the fluid
surrounding it. the computer then needs to solve some very "simple"
differential equations (navier-stokes equations for you physics geeks
like me) that, unfortunately, turn out to be non-linear.
the technique that the article discusses is "meshing", which was the
subject of the plenary talk given by the gentleman from boeing. there's
one or two nice pictures of the mesh for a plane as well as the
supercomputer simulation.
the article mentions that a very good mesh needs about 10^16 points, and
today's supercomputers doing a trillion operations per second needs
about 10^12 years to model ONE SECOND of flight.
really cool article. i'm going to tie this idea from computational
geometry into my class when we discuss bernouli's principle and such
near the end of the year.
hope all is well with everyone.
your pal,
lee