A new computational method that creates a hex-dominant mesh of an arbitrary 3D geometric domain is presented. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh that consists of mostly hexahedral elements with additional prism elements and tetrahedral elements. The proposed method packs rectangular solid cells on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy field that mimics a body centered cubic (BCC) structure, and the cells are moved to stable positions by a physically-based simulation. The simulation mimics the formation of a crystal pattern so that the centers of the cells give ideal node locations for a hex-dominant mesh. The domain isd then meshed into a tetrahedral mesh by the advancing front method, and finally the tetrahedral mesh is converted to a hex-dominant mesh by merging some tetrahedrons.