Repairing Octree Boundary Transition Regions Composed of Different Types of Elements

Abstract

Octree–based algorithms recursively divide the space in 8 or 27 hexahedra (octants). The number of times the split process is applied over an octant is the Refinement Level (RL). When a mesh presents octants of different RL, it is required to manage the transition between fine and coarse regions of the mesh. To do this, transition patterns are applied over octants with neighbors of different RL. When using the 27– split process this can be done only using hexahedra, however in the case of 8–split process this must be done using different types of elements (mixed–elements). The validity of the elements in the transition is ensured when the octant is a regular hexahedron. However, this may not be true when the octant is at the boundary of the domain, specially in concave regions. In this work we introduce a novel node projection technique in order to repair the boundary elements of transition regions in the mesh. Tests results show that, in general, invalid elements can be eliminated without impacting adjacent elements.