Question: is it possible that the box generator generates a patch which does not touch physical boundaries but has ghost cells out of physical boundaries?

Nobody has claimed this yet.

My application needs special treatment when ghost cells out of the physical boundary are used in calculating the fluxes, and for this reason I need to know whether a patch has ghost cells out of the boundary or not.

I use PatchGeometry::getCodimensionBoundaries(int) to determine if a patch touches the physical boundary and in which direction. However, would it be possible that a patch does not actually touch the physical boundary but has ghost cells out of physical boundary?

For example, the index range of the domain is [0, N], and the patch has index range [1, N-1], but a PatchData has ghost width 2.

Start by examining PatchGeometry::getCodimensionBoundaries(int), the box generator, and the relationship between the domain index range, patch index range, and PatchData ghost width. Determine whether a patch such as [1, N-1] with ghost width 2 can have ghost cells outside the physical boundary, then document the answer and the appropriate boundary check for users.

Written by the indexing model from the issue text.