Computer modeling of physical systems

[TheRealColbert]

I am thinking about ways to model physical systems. An example of the type of problem I want to look at would be the response of sound waves to a series of resonators. Here is a java applet of a ripple tank, which is along the lines of what I am thinking of. http://www.falstad.com/ripple/ I expect the things I would like to look at would be intractable from a differential equations approach. Maybe I could do it from a finite element analysis approach, but I think that is beyond my budget, skill and ambition.

So to simplify things, I was wondering if these types of problems can be modeled by creating a series of grids, and making a rule such that each box in the grid uses the state of its neighbors to determine it's own state. Each step in time would allow the wave to "propagate" through the system, and hopefully would exhibit characteristics of the physical system being studied. I think this is kind of like cellular automata. (maybe it IS cellular automata) In any case, what would be the best direction to take to investigate this further? What is it called, and are there key words I could use to search, etc? Is it a dead end?

Some initial problems as I begin to think about it are: How do you deal with the "directionality" of a wave? (ie. if you were modeling a moving ball, you would get stuff flying off everywhere, not a nice, contained moving shape) Also, a square grid isn't isotropic. What problems will that cause when you have a wave or something else going at an angle to the grid.

Any thoughts?

 

[Andy Resnick]

What you describe sounds a lot like "lattice" methods. Fluid flow problems can be modeled well using the lattice-boltzmann method (which is a form of computational fluid dynamics)

http://en.wikipedia.org/wiki/Lattice_Boltzmann_Method

The tricky part, AFAIK, is how to set the mesh size. There are ways to allow the mesh to dynamically adapt to the required accuracy.

http://en.wikipedia.org/wiki/Adaptive_mesh_refinement