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

The 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. Copyright © 2011 John Wiley & Sons, Ltd.