Unstructured three-dimensional mesh generation with controlled anisotropy and directionality

A new computational method for automatic three-dimensional mesh generation is presented. The method creates a high quality mesh and can arbitrarily control anisotropy and directionality of a tetrahedral mesh and a hex-dominant mesh. The hex-dominant mesh can be converted to an all-hex mesh by a set of subdivision templates, called HEXHOOP, that creates a high quality all-hex mesh if the given hex-dominant mesh is of reasonably high quality. The proposed method is based on three new research outcomes: (1) a node-locating algorithm that obtains ideal node locations by packing volumetric cells in the target geometric domain with anisotropy and directionality taken into account; (2) an anisotropic node connecting algorithm using the advancing front method and the local transformation method; and (3) modular templates for hex-dominant to all-hex mesh conversion. Ellipsoidal bubbles are packed in the target domain to obtain ideal node locations for a tetrahedral mesh. The nodes are then connected to yield a tetrahedral mesh with anisotropy taken into account. Similarly, rectangular solid cells are packed in the target domain to obtain ideal node locations for a hex-dominant mesh. The nodes are then connected to yield a tetrahedral mesh, and the tetrahedral mesh is converted to a hex-dominant mesh by merging some tetrahedrons to create hexahedrons and prisms. A hex-dominant mesh can be converted to an all-hex mesh by a set of subdivision templates called HEXHOOP. A subdivision template is built by combining sub-modules, and a template subdivides a hexahedron or a prism into smaller hexahedrons while maintaining the interface conformity with neighboring elements. Tetrahedrons and pyramids included in the hex-dominant mesh are also subdivided accordingly. The proposed method thus covers three major types of finite element meshes; tetrahedral mesh, hex-dominant mesh and an all-hex mesh. It avoids ill shaped elements in a tetrahedral mesh and a hex-dominant mesh induced by badly located nodes. The HEXHOOP templates guarantee the interface conformity of an output all-hex mesh, and it creates a high quality all-hex mesh, providing that the input hex-dominant mesh is of reasonably high quality.