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 socalled 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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