Suppose you have a spherical implosion calculation (e.g. ICF etc.) in which you have a material interface that you want to apply some sort of perturbation to. There are two possible configurations in which the initial material interface is moved inwards/outwards in the radial direction.
From my calculations it would seem that when the interface is further out you don't need as much (angular) resolution to get a converged solution. When the interface is close to the origin you need much more resolution to get a converged solution.
Why is this so? Is it because lengthscales are smaller closer to the origin? I can't seem to find any answers after googling for some time.