I've been looking at the upper
 

I've been looking at the upper triangular ordering of OpenFOAM meshes, and I have a basic question - How critical is it to maintain this during as the solution progresses over time (when topological changes are involved)?

I ask this because I've been making several legal topological changes to my mesh, passed the mapping info into the MotionSolver, and everything still works fine (As in, the motion solver doesn't complain. I'm using Hrv's tetDecomposition method, by the way). A checkMesh call tells me that ordering isn't maintained (as expected, since I didn't know about this requirement before.)

I've read about ordering earlier somewhere in this forum, and by looking at the mesh-files, this is what I've understood:

1. Upper-triangular ordering involves arranging the owners in ascending order (for internal faces alone? Boundary faces don't seem to follow this)

2. Having done that, the corresponding neighbors are to be maintained in ascending order as well.

If this is maintained, it would naturally follow that the cell faces are arranged in the increasing order of neighbors (as explained by Mattjis). I hope I've got this right.
I'm guessing that ordering is a means of achieving efficiency in the matrix-solver? Or is there anything more to it?

Thanks,
Sandeep