UBC Theses and Dissertations

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UBC Theses and Dissertations

The impact of mesh regularity on errors Fan, Hongliang


Mesh quality plays an important role in improving the accuracy of the numerical simulation. There are different quality metrics for specific numerical cases. A regular mesh consisting of the equilateral triangles is one of them and is expected to improve the error performance. In this study, Engwirda’s frontal-Delaunay scheme and Marcum’s advancing front local reconnection scheme are described along with the conventional Delaunay triangulation. They are shown to improve the mesh regularity effectively. Even though several numerical test cases show that more regular meshes barely improve the error performance, the time cost in the solver of regular meshes is smaller than the Delaunay mesh. The time cost decrease in the solver pays off the additional cost in the mesh generation stage. For simple test cases, more regular meshes obtain lower errors than conventional Delaunay meshes with similar time costs. For more complicated cases, the improvement in errors is small but regular meshes can save time, especially for a high order solver. Generally speaking, a regular mesh does not improve the error performance as much as we expect, but it is worth generating.

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