How do compressible fluids differ from incompressible fliuds in terms of their properties?
What is the computational difference? Is vorticity generally faster to model than particular velocity?
@tpan496 An incompressible fluid is something like water that essentially doesn't change volume. As a result, you know that its velocity field must be divergence-free (can't compress or expand), and this assumption can be used to simplify equations or come up with alternative representations that are more amenable to computation. A good example of compressible fluids are gases, which easily change in volume (consider, for instance, the ideal gas law...). Here your solver may have to accommodate effects not seen in incompressible fluids, such as formation of "shocks." Here's an earlier paper on compressible flow simulation in graphics, and a more recent one.
@Kuragama Really depends on the particular phenomenon of interest; the two papers above provide a couple examples.