For most problems, the hanging node adaption provides flexibility for grid adaption. However, the following points should help you in selecting the appropriate type of adaption for your specific application.
The conformal adaption method is only valid for triangular and tetrahedral grids, while the hanging node adaption can be applied to all supported cell shapes.
The hanging node adaption is usually more local in nature than the conformal adaption. In conformal adaption, many cells in addition to the marked cells may be refined due to the longest edge splitting criteria. For highly graded grids, the initial conformal refinement
sweeps tend to exhibit substantial propagation of the cell refinement, sometimes refining the grid many cells away from the actual cell marked for refinement. (Subsequent refinements are usually much more local in nature.) The hanging node scheme only propagates to maintain the refinement level difference, which is much more confined.
Conformal coarsening allows you to coarsen the initial grid, and this is only available in 2D.
With refinement and coarsening, the hanging node adaption scheme will retain the connectivity of the original grid, while the conformal adaption method will modify the connectivity. The modification of the connectivity can have accuracy implications for grids used in unsteady problems with periodic behavior (e.g., vortex shedding behind a cylinder) if you perform successive refinements and coarsenings.
The hanging node adaption has a memory overhead associated with maintaining the grid hierarchy and temporarily storing the edges in 3D. The conformal adaption has no memory overhead other than the additional nodes, faces and cells added to increase the grid density.
Conformal adaption should not be used in conjunction with dynamic adaption (described in Section