Timespace adaptivity
Solving problems in timespace allows for resolving strong timespace anisotropy (as often seen in convective problems) efficiently. The below animation illustrates the concept for a transient 2D viscous fingering problem.
The next animations shows a basic benchmark for circular convection of a circle:
For updates on the state-of-the-art within this research field, I recommend David Darmofal, who has supervised the breakthrough to 4D.