One of the things faster computers mean to physicists is a greater ability to simulate 'chaos' patterns. For example, one of the more difficult things to do quickly enough is the math on weather patterns and the possibilities of tornadoes, hurricanes, etc. Faster computing will help with that I would think.

To explain: take a glass of water. Using an eye dropper let some red food dye drip into the water in the glass. Try to predict where the red will 'go' and what kind of pattern it will make. How will it disperse?

Hell, do the math on billiard balls when the table has weak spots in the cushions. Easy enoug for a single bank shot, but do the math when say three balls are involved. Four. Etc.