Fully‐automated hex‐dominant mesh generation with directionality control via packing rectangular solid cells

Abstract

SUMMARYA new fully automatic hex-dominant mesh generation technique of an arbitrary 3D geometric domain is presented herein. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh consisting mostly of hexahedral elements, with additional prism and tetrahedral elements. Rectangular solid cells are packed on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy ÿeld that mimics a body-centred cubic (BCC) structure (seen in natural substances such as NaCl) and the cells are moved to stable positions by a physically based simulation. The simulation mimics the formation of a crystal pattern so that the centres of the cells provide ideal node locations for a hex-dominant mesh. Via the advancing front method, the centres of the packed cells are then connected to form a tetrahedral mesh, and this is converted to a hex-dominant mesh by merging some of the tetrahedrons.

Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization

“…Once the target vertex density is achieved, adjacent simplicial elements are merged to form cubical ones. Different merging strategies are possible including advancing fronts [14,15,16], graph theory [17] and quality constraints [18,3,4]. Although, some non-cubical elements may remain, particularly in three dimensions, such cubical-dominant meshes are acceptable in many applications.…”

“…An appropriate modification of the proximity-based force used to distribute the mesh vertices indeed enables the partition of the domain into cubical Voronoi regions [3,4]. This improves the local alignment with the metric eigenvectors of the resulting simplices.…”

“…Vertex relocation -A physically-based approach was chosen in the present work [19,20,3,4]. In this paradigm, mesh vertices are particles and the following potential is used to derive the interaction forces between those particles…”

“…Although similar in purpose, the present cubical packing force field was established by a very different reasoning and does not have the same shape than the one proposed in [3,4]. An alignment force is also used to further promote the formation of continuous layers and ultimately increase the percentage of cubical elements in the final mesh.…”

“…Acknowledging this difficulty, cubical-dominant algorithms allow a small percentage of non-cubical elements in order to achieve an increased level of automation. The present work proposes such an algorithm that combines cubical particle packing [3,4] Quad-dominant, mesh adaptation, anisotropic Riemannian metric.…”