[CA models of fluids: a notebook of programs and references] - A New Kind of Science: The NKS Forum

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

Posted by: Richard Phillips

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

Posted by: Jason Cawley

Very nice stuff, Richard, thanks...

Posted by: A.Shankar Ananth

Wonderful work. A must know for Chemical Engineers like me

Posted by: Peter Laurie

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?

Posted by: Peter Laurie

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

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

Posted by: Richard Phillips

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.

Posted by: Todd Rowland

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