Adaptive hexahedral mesh generation and regeneration using an improved grid-based method

Abstract

An improved grid-based algorithm for the adaptive generation and regeneration of hexahedral element mesh is presented in this paper. The method for the mesh density generation and control is introduced. The refinement field is generated based on the surface curvatures, geometry features, density windows and field variables distribution. To give good description of the geometry features, eight different types of free element facet configurations are given for the mesh matching to the surface of the solid model. Scaled Jacobian and the Condition Number of the Jacobian matrix are used to evaluate the hexahedral element mesh quality. A curvature-based Laplacian smoothing approach is employed to improve the quality of boundary elements and preserve the boundary characters of mesh. To improve the quality of the surface meshes and the interior elements, an optimization approach is proposed by using mesh quality metric as the objective function. By combining the Laplacian smoothing method with the optimization approach, the mesh quality is improved significantly. For the surface meshes, the Condition Number of a set of Jacobian metric associated with the quadrilateral elements is taken as the optimization objective function. For the interior elements, the Condition Number metric associated with the hexahedral elements is employed as the optimization objective function. The effectiveness and robustness of the approaches are demonstrated through two complex three-dimensional models.