23 although these transformations are simple they

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Unformatted text preview: to map relatively complex two- and three-dimensional regions. Two examples involving the ow about an airfoil are shown in Figure 5.2.4. With the transformation shown at the top of the gure, the entire surface of the airfoil is mapped to = 0 (2-3). A cut is made from the trailing edge of the airfoil and the curve so de ned is mapped to the left ( = 0, 2-1) and right ( = 0, 3-4) edges of the computational domain. The entire far eld is mapped to the top ( = 1, 1-4) of the computational domain. Lines of constant are rays from the airfoil surface to the far eld boundary in the physical plane. Lines of constant are closed curves encircling the airfoil. Meshes constructed in this manner are called \O-grids." In the bottom of Figure 5.2.4, the surface of the airfoil is mapped to a portion (2-3) of the axis. The cut from the trailing edge is mapped to the rest (1-2 and 3-4) of the axis. The (right) out ow boundary is mapped to the left (1-5) and right (4-6) edges of the computational domain, and the top, left, and bottom far eld boundaries are mapped to the top ( = 1, 5-6) of the computational domain. Lines of constant become curves beginning and ending at the out ow boundary and surrounding the airfoil. Lines of constant are rays from the airfoil surface or the cut to the outer boundary. This mesh is called a \C-grid." 5.2.2 Unstructured Mesh Generation There are several approaches to unstructured mesh generation. Early attempts used manual techniques where point-coordinates were explicitly de ned. Semi-automatic mesh generation required manual input of a coarse mesh which could be uniformly re ned by dividing each element edge into K segments and connecting segments on opposite sides of an element to create K 2 (triangular) elements. More automatic procedures use advancing fronts, point insertion, and recursive bisection. We'll discuss the latter procedure and brie y mention the former. With recursive bisection 3], a two-dimensional region is embedded in a square \universe" that is recursively quartered to create a set of disjoint squares called quadrants. Quadrants are related through a hierarchical quadtree...
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.

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