Among the more esoteric simulators are a class of programs called Finite Element Analysis (FEA) engines. One reasonably powerful one is Quickfield. (www.quickfield.com).
You can download a "free" student version that is limited not in what it can do, but by how many elements (and thus the overall exactness) it will resolve to.
This solves non-linear magnetics problems and describes how the fields flow in mixed air-magnetic material systems, along with multiple types of non-linear magnetics. Thus you can see the fields flowing in a transformer made up of an air gap, and mixed nickel and cobalt material (for instance).
The electrostatic part allows you to model the fields inside a tube.
There is a tutorial to help get you started.
Just FYI
-Steve