Quality improvement methods for hexahedral element meshes adaptively generated using grid‐based algorithm

Abstract

SUMMARYThe quality of finite element meshes is one of the key factors that affects the accuracy and reliability of numerical simulation results of many science and engineering problems. In order to solve the problem wherein the surface elements of the mesh generated by the grid-based method have poor quality, this paper studied mesh quality improvement methods, including node position smoothing and topological optimization. A curvature-based Laplacian scheme was used for smoothing of nodes on the C-edges, which combined the normal component with the tangential component of the Laplacian operator at the curved boundary. A projection-based Laplacian algorithm for smoothing the remaining boundary nodes was established. The deviation of the newly smoothed node from the practical surface of the solid model was solved. A node-and area-weighted combination method was proposed for smoothing of interior nodes. Five element-inserting modes, three element-collapsing modes and three mixed modes for topological optimization were newly established. The rules for harmonious application and conformity problem of each mode, especially the mixed mode, were provided. Finally, several examples were given to demonstrate the practicability and validity of the mesh quality improvement methods presented in this paper.

A consistent octree hanging node elimination algorithm for hexahedral mesh generation

“…Ito et al [11] proposed a solution for 2D convexity embedded in 3D meshes by a new template mimicking a pillowing [15] of one element. Similarly, Sun et al [18,19] proposed a set of refinement templates which have many common features with those proposed by Ito et al [11] with the addition of two corner refinement templates. However, the quality of these transition elements is questionable.…”

“…The method of Parrish et al [12] is directional and the resulting mesh is not symmetric for a symmetric refinement field and depends on the order of operations. It is observed that all these methods [12,11,18,19] introduce smallsized elements at the corner of concavely refined regions. Similarly, methods that rely on the dual contouring [20] might also introduce elements at the coarse/fine mesh interface that have smaller feature size than that of the fine refinement field.…”

Research on the Algorithm for Grid-Based Hexahedral Mesh Generation of CAD Assembly Models

“…Among them, Step 1 ~ Step 4, Step 7 see the reference literature [8][9][10][11][12][15][16][17], this paper will not repeat them.…”

“…In recent years, many scholars have studied the gridbased hexahedral mesh generation algorithms for simple geometry models, and made some great results [8][9][10][11][12], but the research on CAD assembly models is very few, the main reason is that the geometrical characteristics of the CAD assembly models are much more complicated than the simple geometry models, especially the presence of the interface, resulting surface matching and quality optimization algorithms in hexahedral mesh generation need to do special treatment. Zhang [13] proposed a full hexahedral mesh generation algorithm using grid-based method for the CAD assembly models.…”

Hex-Mesh Generation and Processing: a Survey

“…Thus such research often focused on meshes with nearregular connectivity. For instance Sun et al [2012] propose an optimization method specific for grid-based meshes that employs a combination of modified Laplacian smoothing and topological operations on the padding layer of the input mesh. The method is demonstrated to work on simple inputs; thus its applicability in the general case remains to be tested.…”