The von Neumann stability analysis is a great tool to assess stabilty of discretizing schemes for PDEs. But too often, imho, the discussion gets blurred with trigonometric expressions. Here, I try to provide a shortcut.
BTW: it’s “fon no ee man”
The Rayleigh-Taylor instability is a well-known benchmarck for CFD codes. The idea is to start with two phases, on on top of the other, the lighter one being underneath. The interface is slightly perturbed, and this plume appears. I describe a quick and dirty way of getting this instability.