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Quadrants are related through a hierarchical quadtree

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Unformatted text preview: structure. The original square universe is regarded as the root of the tree and smaller quadrants created by subdivision are regarded as o spring of larger ones. Quadrants intersecting @ are recursively 6 Mesh Generation and Assembly η 4 1 11111111111 00000000000 11111111111 00000000000 11111111111 00000000000 3 11111111111 00000000000 11111111111 00000000000 2 4 1 ξ 2 6 5 11111111111 00000000000 11111111111 00000000000 11111111111 00000000000 3 11111111111 00000000000 11111111111 00000000000 2 4 1 airfoil 3 11111111111111111111111111 00000000000000000000000000 η 6 11111111111111111111111111 00000000000000000000000000 ξ 5 1 2 airfoil 3 4 Figure 5.2.4: \O-grid" (top) and \C-grid" (bottom) mappings of the ow about an airfoil. quartered until a prescribed spatial resolution of is obtained. At this stage, quadrants that are leaf nodes of the tree and intersect @ are further divided into small sets of triangular or quadrilateral elements. Severe mesh gradation is avoided by imposing a maximal one-level di erence between quadrants sharing a common edge. This implies a maximal two-level di erence between quadrants sharing a common vertex. A simple example involving a domain consisting of a rectangle and a region within a curved arc, as shown in Figure 5.2.5, will illustrate the quadtree process. In the upper portion of the gure, the square universe containing the problem domain is quartered creating the one-level tree structure shown at the upper right. The quadrant containing the curved arc is quartered and the resulting quadrant that intersects the arc is quartered again to create the three-level tree shown in the lower right portion of the gure. A triangular mesh generated for this tree structure is also shown. The triangular elements are associated with quadrants of the tree structure. Quadrants and a mixed triangularand quadrilateral-element mesh for a more complex example are shown in Figure 5.2.6. Elements produced by the quadtree and octree technique...
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