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Re: Fluid dynamics

• To: mathgroup at smc.vnet.net
• Subject: [mg44530] Re: Fluid dynamics
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 13 Nov 2003 05:57:49 -0500 (EST)
• Organization: The University of Western Australia
• References: <boif5j$oau$1@smc.vnet.net> <bopc55$olh$1@smc.vnet.net> <botced$chd$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <botced$chd$1 at smc.vnet.net>,
 Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote:

> oh with 
> 
> "why not _start_ with a
> cellular automata, modeling the 
> microscopic behavior of fluid molecules"
> 
> you can also make a cow from the beef ?

For an intelligent person, Jens, it seems you have missed the whole 
point of NKS.
 
> The Naver-Stokes equation is an approximation,
> a numerical model is an approximation to this
> approximation and a CA is an approximation to this
> approximation. 

No, No, No ... 

> And now tell me why the approximation,
> of the approximation, of a approximation is a good
> starting point to describe the *real* process without
> an approximation.

Because this is _not_ what NKS is proposing. 
 
> Where is the source of all the information that is
> lost in during the various approximations if you start
> not with the original ?

But what is the original? It is not, as you describe it, the 
Navier-Stokes equation.

> In a real collision the scattering take not place
> on a hexagonal grid, and the scattering directions are
> not bounded on a grid. 

Agreed. The CA model on a hexagonal grid is an approximation.

> The *only* reason to use a CA is, that a CA has excelent
> properties for massive parallel computing. 

This is _not_ the only reason to use CA.

> And it is realy surprising that such a lausy model has still some
> (qualitative) features of the real process. However,
> in the most cases the quatitative computed features, like
> pressure differ significant from the measured ones or from
> the computed values obtained by a FE solution.
> 
> Starting with a CA and use it for the real process is like to take
> the a photograph of an image of a painted apple and eat it.

It seems like you are still stuck in the world of continuum models ...

Anyway, http://forum.wolframscience.com is probably a better place to 
discuss this topic.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
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