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We revisit the generation of balanced octrees for adaptive mesh refinement(AMR) of Cartesian domains with immersed complex geometries. In a recent shortnote [Hasbestan and Senocak, J. Comput. Phys. vol. 351:473-477 (2017)], weshowed that the data-locality of the Z-order curve in hashed linear octreegeneration methods may not be perfect because of potential collisions in thehash table. Building on that observation, we propose a binarized octreegeneration method that complies with the Z-order curve exactly. Similar to ahashed linear octree generation method, we use Morton encoding to index thenodes of an octree, but use a red-black tree in place of the hash table.Red-black tree is a special kind of a binary tree, which we use for insertionand deletion of elements during mesh adaptation. By strictly working with thebitwise representation of the octree, we remove computer hardware limitationson the depth of adaptation on a single processor. Additionally, we introduce ageometry encoding technique for rapidly tagging the solid geometry forrefinement. Our results for several geometries with different levels ofadaptations show that the binarized octree generation outperforms the linearoctree generation in terms of runtime performance at the expense of only aslight increase in memory usage. We provide the current AMR capability asopen-source software.

Binarized octree generation for Cartesian adaptive mesh refinement around immersed geometries