I'm working with the OpenFOAM C++ Computational Continuum Mechanics library (it can deal with fluid-solid interaction, MHD flows...) which uses arbitrary unstructured meshes. This was driven by the idea of using the advantage of fast generation (automatic usually) of unstructured meshes to simulate problems in complex geometries.
However, recently I've encountered another approach: octree adaptive carthesian meshes with cell "cutting", where the agressive mesh refinement is used to describe a complex geometry.
From the standpoint of the numerics, Carthesian meshes are much more accurate, so my question is: has anyone experience in using/implementing one or both of these approaches? How do they compare agains each other?
I'm developing codes for two phase fluid flow and I noticed e.g. that the reconstruction of the field gradients can be easily made more accurate on Carthesian meshes, while unstructured mesh requires linear regression for abrupt changes in the field...