One of the most common uses for HPC is modeling fluid flow. This general class of models has a wide range of applications, including weather forecasting, hydraulics, blood flow, etc. When modeling fluid flow, we cannot simply divide the volume into sectors and model flow independently in each sector, since some fluid flows across the boundaries between neighboring sectors. If one process models each sector, each process must exchange some information with the processes modeling neighboring sectors in order to account for all of the fluid in the system.
Another common use for HPC is finite element analysis. Finite element analysis is used to solve partial differential equations, often to model engineering simulations. There are many open source and commercial finite element software packages that utilize HPC.