Here's where I have to confess to ignorance, being an experimentalist who normally doesn't have to deal with this problem. I think their model involves describing particle interactions in extremely large matricies (somehow different from the standard way of doing it, I don't know how). As such, they may need to perform large-scale matrix inversions in order to do a calculation, which are perhaps the most computationally intensive projects known to mankind. Since they may be trying to simulate production at the LHC at some level, this could be a lot of matricies to invert. This is why they need brute power instead of finesse.

However, I'm not sure. I just know that they need a lot of teraflops.