Computationally Intractable (or maybe not?)

26 03 2011

In Bussard’s 2006 Google tech talk  Should Google Go Nuclear? he talks about computer modeling of his reactor. He concludes that computer modeling is unfeasible. Beyond a handful of particles in the model, the computation slows down to the point of useless.

Now there may be a new approach to this type of problem.

http://news.stanford.edu/news/2011/march/airplane-aeroelastic-flutter-032411.html

Professor Charbel Farhat, chair of the Aeronautics and Astronautics Department at Stanford’s School of Engineering, and David Amsallem, an engineering research associate who worked on his PhD thesis with Farhat, have been studying and trying to solve aeroelastic flutter for years. Computers help, but only to a point.

Essentially it’s a story of the unfeasible made feasible by mathematical inovation:

How have Farhat and Amsallem succeeded where others have come up short? The answer sounds suitably complex: interpolation on manifolds. What it means, in essence, is approximating unknowns based on known information. The two engineers devised a system of mathematical approximations that break down complex, computationally demanding equations into smaller, more manageable parts. In mathematics, this is known as “reducing.” Reducing allows them to make some very educated guesses, very quickly.

I wonder if this technique could be applied to computer modeling of the Bussard reactor?

I suppose in our case we would be looking FOR the flutter, not trying to avoid it.

UPDATE:

Another good article: http://www.psc.edu/science/2001/farhat/

One response

27 03 2011

The “reduced order modeling” would be good to make a design code for exploring reactor configurations once you had a high-fidelity predictive code or lots of experimental data for lots of configurations. In your case, getting that foundational simulation or experimental database is the hard part. Fast multi-dimensional interpolation after that is just sizzle for your steak.

The ideas from the moving grid stuff (mentioned in the second article) from this sort of aeroeleastic simulation could be good for “grid adaption” in a plasma model. I haven’t looked at this literature in about five years (Farhat’s papers stood out to me then), but I recall the “spring analogy” being popular for getting a governing equation for the grid. You probably want something different for your plasma simulation, since it is solution accuracy you want to improve, rather than tracking moving boundaries (some sort of diffusion equation forced by an error or “monitor” function would make sense, here’s a simple example).

I *think* the problem Bussard was addressing is that this plasma spans the boundaries between suitable governing equations / solution methods. You probably need some sort of hybrid particle / fluid code, or different models for different zones of your device (which you could think of as a way towards “reduced order modeling” by decomposing the problem). If you are serious about doing a simulation, CLAWPACK would probably be a good place to start learning. It’s been successfully applied to lots of different equations sets (very general finite volume based approach).