This is what used to be called supercomputing, but since a lot of it is done on clusters of fairly ordinary computers these days, the word HPC has gained currency.

Typical scientific applications include:

• astrophysics (e.g., simulations of a supernova explosion or black hole collision)
• automotive/aerospace industry (e.g., simulations of a car crash or a new airplane design)
• climate modeling (e.g., simulations of a tornado or prediction of the earth's climate for the next century)
• economics (e.g., modeling the world economy), etc.
  

An example is Distributed Interactive Simulation (DIS), a technique used for training and planning in the military field. Realistic scenarios may involve hundreds of thousands of entities, each with potentially complex behavior patterns. Today, the largest supercomputers can handle at most 20,000 entities.