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Implementing a Node Based Split-Tree Search Algorithm

Vincent C. Betro and Steve L. Karman, Jr.

Research Notes, 19th International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 3-6 2010

IMR
PROCEEDINGS

19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

University of Tennessee at Chattanooga SimCenter, 701 E. MLK Blvd., Chattanooga, TN, 37403.
Email: Vincent-Betro@utc.edu
University of Tennessee at Chattanooga SimCenter, 701 E. MLK Blvd., Chattanooga, TN, 37403.
Email: Steve-Karman@utc.edu

Summary
Cartesian hierarchical meshes are becoming a central focus of grid generation research since they are rapid to generate [1], they can refine in pertinent areas to a desired resolution [2], and they provide an excellent basis for mesh adaptation [3]. More importantly, having a Cartesian hierarchical mesh allows for the natural creation of a tree, often an Omni-tree or an Octree, which aids in searching for elements as well as only needing to remesh certain branches for dynamic meshing. Generating a Cartesian hierarchical mesh requires the creation of a root cell around the geometry to be meshed. Then, through recursive refinement, the root cell volume is discretized by creating successively smaller volumes, often utilizing some method of preserving spacing, such as Riemannian Metric Tensors [4]. Finally, cells outside of the computational domain are turned o , and a body conforming volume mesh, overset mesh, or immersed boundary formulated mesh is created. The basic building block for a Cartesian hierarchical mesh is a voxel [5]. Each voxel contains the index of its mother voxel, and the root voxel is the only voxel without an initialized mother; it also contains a list of its children, if they exist. A split variable may also be given in the structure (except in the case of an Octree, since refinement is isotropic), wherein the direction of refinement is stored for ease of tree traversal. Also, the physical coordinates of the high and low corner points of the voxel are stored for construction of the physical points after the mesh is generated and for relative tree traversal purposes [6] .

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