the triangular mesh 

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... Figure 49 shows the triangular mesh. Figure 50 shows the IPython window output generated during the final smoothing operations of this mesh. The author also switched-on an option to show the list of ‘not so good triangles’, their exact position in the triangular mesh and their characteristics. As one can see, smoothing improved the minimum q in the mesh from 0.32 to 0.49 and the minimum interior angle of the triangles from 22.6 to 24.0 degrees. The number of ‘not so good triangles’, defined as those with q < 0.6 decreased from 168 to 5, and the number of ‘not so good triangles’ defined now as those with an interior angle less than 30 degre es decreased from 222 to 13. How do the ‘not so good triangles’ really look in practice? The line before the last in the print out says that the triangle with worst q (q = 0.49) was the triangle number 8854 comprised of the nodes numbered 4883, 4874 and 5839 and in the last three columns it gives the coordinates of the nodes of this triangle. With this information we can easily go to the plot of the triangular mesh, zoom- in and locate the ‘worst’ triangle. This worst triangle appears close to the head of the slat and is shown in Figure 51. A zoom-in is provided in Figure 52. Notice that in this region the size of the triangles changes, perhaps, too fast. Hence, we might eliminate this worst offender by either increasing the size of the external elliptic boundary (put it further away) to allow for a more graded variation in triangle size when moving from the internal to the external boundary or by increasing the number N of nodes on the external boundary. Figure 53 gives the complete mesh, including both the quad meshes and the triangular mesh. Figures 54-58 zoom on interesting regions of the mesh to get a better feeling of the geometric characteristics of the interface between the quads and the triangles. This paper describes in detail an approach for hybrid meshing in 2D. It uses the proven algorithms presented in the seminal papers by Steger and Chausseau [5] and Frey [12]. It presents and explains an original algorithm developed by the author to deal with acute convex and concave points in a structured mesh and provides multiple examples of the application of this algorithm (clearly, this algorithm can also be applied to 3D structured meshes). The approach taken in this paper is practical and, therefore, significant time is devoted to problems on how to evaluate the quality of the generated grids and verify their integrity. A significant number of examples using actual airfoils were given and intuitive explanations of the working of the algorithms were added to make it more accessible to a general audience. The paper is directed specially to students, CFD practitioners and even the occasional Physicist who just wants to check a new idea without having to invest countless time and money in proprietary meshing tools. Python 2.7.3 was used. For expediency, the author purchased the package provided by Enthought. The installation takes only a couple of minutes and you can begin working. However, the author – on purpose - used from this package only the standard Python, Numpy and Matplotlib modules, and these can be downloaded directly from the Python and SciPy organizations. A copy of the code used in this paper can be obtained for free from the author by instructors at educational institutions teaching a CFD course, as an additional help to their course. The use of this paper and code for educational purposes, and the distribution and reproduction of the paper in any medium is allowed, provided the original author and source are clearly and explicitly credited. My thanks to Starbucks for providing the anonymity and the quiet environment needed for this ...