Test curvatures/ad_curvatures

[lindsayad]

Rationale

The correctness of the signs of curvatures and ad_curvatures needs to be verified.

Description

Libmesh has calculations of curvatures and now in MOOSE we have corresponding calculation of ad_curvatures. In the curvature calculation code it is noted that the sign of the curvature (e.g. the convention) is different between 2D and 3D. We really want to make this dimension agnostic, consistent with other MOOSE practices. So we need to verify that with the same set of kernels in 2D and 3D we can correctly model the effect of curvatures in things like surface tension forces.

Impact

Confidence in curvature calculations

[lindsayad]

The tests added in #24204 show that a surface which curves in the opposite direction of the normal produces a positive curvature for 3D and negative curvature for 2D. We can hope that the converse is true, e.g. for a curve which curves in the same direction as the normal, we will see a positive curvature for 2D and negative curvature for 3D. This is consistent with @jwpeterson's comment in #17183 (reply in thread). In libMesh/libmesh#3560 we will make the 2D convention the convention, with the proper deprecation process. E.g. we will need a deprecation process to keep libMesh CI green after the merging of #24204