Generation of Cut- and Split-Cells for Face-Piercing Geometry in Embedded-Boundary Cartesian Methods

This innovation addresses several critical issues in the construction of cut control volumes using embedded-boundary Cartesian mesh generators. The innovation considers the case of a surface triangulation intersecting the face of a Cartesian hex without intersecting any of its edges. Such face-piercing geometry is common in practical applications, especially when surface variations occur on a smaller scale than the Cartesian hex dimensions, i.e. coarse meshes. Examples include geometric perturbances such as nozzles, or even minor surface undulations and dimples. Furthermore, the innovation also considers the case of a surface triangulation containing internal passages within the Cartesian hex. The innovation correctly handles situations where hexes split into multiple control volumes are merged together if internal connections exist within the surface.