Supercomputers, fluid dynamics

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

Hello all,

I'm studying supercomputers, but I am wondering about the mathematics
problems that would require them. I understand that many of the
problems that are run on them are fluid dynamics, but I don't quite get
what could make these problems so incredibly complicated that they need
to run on 100 computers in parallel for several days. What do all the
variables represent? I found a website online that seemed to indicate
that fluid dynamics problems are relatively easy when you just have
fluids, but becomes very hard when there are chunks of solid matter
involved. For instance, blood has lots of solids in it, and that's why
it's much more complicated to calculate with than water. Is that true?
It still seems outrageous how difficult these problems are. Does anyone
want to give a lecture on this? I promise to read whatever you post.

Greg

Shlomo Kashani · science forum beginner Joined: 18 Jun 2006 Posts: 7

I know they are in use for the simulation of global illumination of
fluids.

See for instance: http://www.csit.fsu.edu/~beason/thesis/

:)

gmarkowsky@gmail.com wrote:

Roy Stogner · science forum beginner Joined: 13 Jun 2005 Posts: 38

On Mon, 19 Jun 2006 12:09:05 -0700, gmarkowsky wrote:

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

Thank you for your replies, and for the links. They both are
interesting and I'll have to spend more time on them. As for my math
background, it's better than average in that I have a Ph.D. in math Smile

but I have concentrated on the pure stuff and am only now starting to
drift into the more applied fields. Anyway, I know about ODE's and
PDE's, so if one wants to do more than hand wave I can follow it I
believe.

Tom · science forum Guru Wannabe Joined: 21 Jan 2006 Posts: 173

You seem to think that the problem needs to be really complicated to require a supercomputer...
All you need is a problem that needs high accuracy/resolution.. it doesn't have to be complicated equations.

For example, you could model weather using the Navier-Stokes equations (about 5 differential equations per point), but you'd need a point perhaps every meter... so modelling the weather for UK would require about 1000000*500000*10000 points.
Ie making problems that need supercomputers is easy, not difficult.
Whats difficult is making the problems solvable even on supercomputers.
So weather modelling calculations have to resort to more complex (approximating) equations that work on larger areas (eg complex algorithms for modelling a cubic kilometer of weather), you then only need to simulate 1000*500*10 points.

In other words, its not the complicated equations that necessitate the supercomputer... its the high accuracy that necessitates the complex equations (and the supercomputer).

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

Is the problem that the Navier-Stokes theory isn't complete? Because
one can get a very accurate answer, even sometimes an exact answer, on
one desktop to many differential equation problems. Is the problem that
we have no good ways of dealing with N-S equations so that we have to
resort to brute force?

Greg

Tom wrote:

Gerard Kramer · science forum beginner Joined: 11 Jun 2006 Posts: 11

In a sense, yes.

Have a look at http://www.claymath.org/millennium/Navier-Stokes_Equations/

Indeed, it's one of the Clay institute's "millenium problems". So apart
from the practical side of fluid dynamics there are still important
well-posedness questions to be dealt with. If you're looking for a
challenge.. ;-)

For this you could perhaps also refer to J.C. Robinson,
Infinite-Dimensional Dynamical Systems etc. Cambridge University Press
(2001).

gmarkowsky@gmail.com wrote:

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

Thanks for all the replies, very helpful. Yeah, maybe I'll try to fix
up the Navier-Stokes theory tonight before I go to bed, I could use a
million dollars.

Greg

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

By the way, how does one pronounce "Navier" as in Navier-Stokes
equations? Don't want to make a fool of myself when I talk to someone
about this.

Greg

Dan Nagle · science forum beginner Joined: 16 Mar 2006 Posts: 2

Hello,

gmarkowsky@gmail.com wrote:

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

Thanks. Yeah, I remember being surprised when I learned it's pronounced
"Oiler". So the r is silent in Navier, but is it NAV ee a or nav EE a?
I'm guessing the latter.

Greg
Dan Nagle wrote:

Dave Seaman · science forum Guru Joined: 24 Mar 2005 Posts: 527

On 22 Jun 2006 08:07:34 -0700, gmarkowsky@gmail.com wrote:

gmarkowsky@gmail.com · science forum beginner Joined: 07 Nov 2005 Posts: 18

Many thanks.

Greg

Dave Seaman wrote:

Ronald Bruck · science forum Guru Joined: 05 Jun 2005 Posts: 356

In article <1150744145.027452.178800@u72g2000cwu.googlegroups.com>,
<gmarkowsky@gmail.com> wrote:

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