Smoothing and untangling for polyhedral mesh based on element shape transformation

Mesh smoothing is a critical technique for enhancing mesh quality. Recently, polyhedral meshes have gained prominence in Computational Fluid Dynamics (CFD), with orthogonality being a common metric for evaluating these meshes. This paper introduces an innovative geometric method for smoothing and untangling polyhedral meshes, leveraging element shape transformation to improve orthogonality. The proposed method involves two primary operations. The first operation enhances individual element quality through geometric shape transformation achieved by node movement. This movement direction is determined by a combination of the node's normal vector and a correction vector. Following this transformation, temporary nodes of each element are established, and the node positions are updated using a weighted average of their corresponding temporary node set, a process referred to as element stitching. These operations can be iteratively applied to progressively enhance overall polyhedral mesh quality. The effectiveness and stability of this method are demonstrated through various examples, showing not only an improvement in mesh quality but also the elimination of inverted elements. CFD simulation results further indicate that the enhanced mesh quality positively impacts simulation accuracy.