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Richard Phillips
Wolfram Science Group
Boston, USA

Registered: Oct 2003
Posts: 46

CA models of fluids: a notebook of programs and references

Attached is a notebook containing Mathematica programs, and literature references, that may help to understand how to do CA fluid dynamics. The main text section in the book that talks about this is:
http://www.wolframscience.com/nksonline/page-376

Attachment: cellularautomatonfluids.nb
This has been downloaded 3097 time(s).

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Old Post 03-27-2004 11:46 PM
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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Very nice stuff, Richard, thanks...

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Old Post 03-28-2004 02:48 AM
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A.Shankar Ananth
Anna University
INDIA

Registered: Jul 2004
Posts: 2

Re: CA models of fluids: a notebook of programs and references

Wonderful work. A must know for Chemical Engineers like me

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Old Post 07-07-2004 12:12 PM
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Peter Laurie
A L Systems
Dorset, UK

Registered: Mar 2005
Posts: 3

Boat wakes

I found the vortex street on p 380 of NKS very astonishing and I was thinking of trying the method on the movement of a boat across the surface of water. The wake is very complicated.

This may take more than an afternoon!

If anyone has any interest in this project, maybe we could collaborate?

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Old Post 03-13-2005 11:38 AM
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Peter Laurie
A L Systems
Dorset, UK

Registered: Mar 2005
Posts: 3

anotherway of doinf finite element analysis?

Is there anything fundamentally different between this and finite element analysis?

I expect I've missed something. Maybe the bit of randomisation?

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Old Post 03-13-2005 02:58 PM
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Richard Phillips
Wolfram Science Group
Boston, USA

Registered: Oct 2003
Posts: 46

Yes, I think the two methods are rather different.

The CA (or "lattice gas") model uses many, many very simple idealized particles, and at a much larger scale than the particles you see continuous looking fluid motion. It takes many millions of these particles to simulate even quite small parts of a fluid. No conventional continuous math like differential equations is involved (at least in the model itself). This is really different from conventional numerical approximations to continuous mathematics.

Generally finite element models split up space into small patches and approximate each using conventional continuous math, getting systems of equations out, to solve using numerical methods. These patches are relatively much larger than the cells in the CA.

Here's a short description of finite elements:
http://mathworld.wolfram.com/FiniteElementMethod.html

Another popular method is so-called Lattice Boltzmann methods which very roughly speaking are half way between things like the CA models and the numerical methods.

Perhaps you mean something deeper by "fundamentally different" but the construction of the models certainly is.

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Old Post 03-16-2005 07:05 PM
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Todd Rowland
Wolfram Research
Maryland

Registered: Oct 2003
Posts: 113

updated for version 8

I've updated the Arrow and other code so this will work in version 8.

Attachment: cellularautomatonfluids.nb
This has been downloaded 389 time(s).

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Old Post 06-19-2012 02:04 PM
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