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MathGroup Archive 2003

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Re: Re: Fluid dynamics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44555] Re: [mg44530] Re: Fluid dynamics
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 14 Nov 2003 01:58:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I think, at this point, this dispute is essentially about philosophy. 
Are discrete models approximations of continuous reality or continuous 
models of a discrete one?
Actually, it's only a part of the problem. In economics and finance the 
situation is clearer: there is no doubt that "the reality" in this 
field is discrete but continuous models dominate since they are both 
much easier for humans to handle and can be used to reduce the 
complexity of the problem one is trying to solve before the final 
"discretization" is made for the purpose of computation. I have been 
wonderting myself if cellular automata could be useful in this field, 
but as far as I can tell they suffer form the same problems as other 
discrete models. But then I am sure I have not given this matter enough 
thought.

Andrzej


On 13 Nov 2003, at 19:57, Paul Abbott wrote:

> 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
> School of Physics, M013                         Fax: +61 8 9380 1014
> The University of Western Australia      (CRICOS Provider No 00126G)
> 35 Stirling Highway
> Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
> AUSTRALIA                            http://physics.uwa.edu.au/~paul
>
>
>


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