Quality improvement method for graded hexahedral element meshes

A procedure is presented to improve the quality of hexahedral element meshes, especially for the meshes adaptively generated using a modified grid-based method. Insertion technique and collapsing technique are proposed to modify the mesh topology and improve the quality of the degenerated elements which are on the mesh boundaries and cannot be improved by any nodes position smoothing methods. A curvature-based Laplacian smoothing method is employed to improve the shape-quality of boundary elements and ensure that the boundary characters of mesh are well preserved. A method for improving the shape-quality of the mesh surface and the initial elements which is based on the objective function of the mesh quality metric is proposed. For the mesh surface, the Condition Number of the Jacobian metric associated with the quadrangle elements is taken as the optimization objective function. For the initial elements, after smoothing with the Laplacian method, the Scaled Jacobian metric associated with the hexahedral elements is employed as the optimization objective function. The proposed optimization methods have been applied to the adaptive generation of the hexahedral element mesh using grid-based method. The effectiveness and robustness of the proposed optimization methods are tested through several complex three-dimensional models.