Volume preservation improvement for interface reconstruction hexahedral methods

We propose a new post-processing procedure for automatically adjusting node locations of an all-hex mesh to better match the volume of a reference geometry. Hexahedral meshes generated via an overlay grid procedure, where a precise reference geometry representation is unknown or is impractical to use, do not provide for precise volumetric preservation. A discrete volume fraction representation of the reference geometry MI on an overlay grid is compared with a volume fraction representation of a 3D finite element mesh MO. This work proposes a procedure that uses the localized discrepancy between MI and MO to drive node relocation operations to more accurately match a reference geometry. We demonstrate this procedure on a wide range of hexahedral meshes generated with the Sculpt code and show improved volumetric preservation while still maintaining acceptable mesh quality.