Mesh refinement is one of the core components of mesh adaptation. This paper presents an adaptive refinement method based on edge subdivision for unstructured meshes, which incorporates element quality control. The refinement applies isotropic subdivision to target elements and anisotropic subdivision to transition elements. To support mesh refinement, we summarize all topologies of tetrahedra, pyramids, and prisms with hanging nodes, and over half of topologies of hexahedra with hanging nodes. These topologies fall into two kinds: allowable subdivision types, which possess the corresponding subdivision templates; forbidden subdivision types, which can be converted into the former via an additional edge subdivision strategy. Boundary layer mesh refinement with preservation of the layered structures of specified layers can be achieved in the presented method. An element quality control mechanism is introduced in the refinement of transition elements. It takes into account three quality metrics: warpage, skewness, and aspect ratio. The simulation results demonstrate that the proposed method is universally applicable to unstructured meshes consisting of standard elements, and is capable of preserving the layered structures of boundary layers. Furthermore, it can reduce the refinement propagation into non-target regions, and mitigate the rapid deterioration of mesh quality.
CHEN et al. (Sun,) studied this question.
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