Sunday, August 26, 2012

Mesh quality measures for 2d meshes


Mesh quality measures for 2d meshes

There are several methods to measure the quality of a mesh element (cell). The quality of a cell is measured with respect to a reference element (cell) that is claimed to have the best quality. The reference element is dependent on the application where this mesh is going to be used. Therefore, there is no absolute definition of mesh quality. Considering the applications of multi-physics simulation, the mesh elements (cells) are required to be almost uniform. For a 2d case, the triangular cell is required to be an equilateral triangle, the quad element is required to be a square, and so on. The following are some techniques to measure mesh quality:

1.   Minimum angle criteria

Quality is measured based on a predefined optimum value of minimum angle.

2.   Maximum angle criteria

Quality is measured based on a predefined optimum value of maximum angle.

3.   Perimeter and area criteria

The quality is measured as the ration between the square of perimeter divided by the area of the element. This method is suitable for any polygon element. An additional advantage is that this method can be used for mixed-element meshes.

4.   Inscribed and circumscribed circles criteria

In fact, this method can be used only with triangular elements. The quality is defined as radius of the circumscribed circle divided by radius of the inscribed circle.

5.   Perimeter and edge ratio criteria

This method also is used only for triangular elements. For any cell compute the perimeter and divide it by number of edges of the cell to get edge length of the uniform polygon having the same perimeter (reference edge length). Then get the ratios of edge lengths to the reference edge length. Finally, compute the arithmetic average of these ratios to get the quality of this cell.

6.   Edge ratio criteria

Used for triangular cells. Quality is the ratio of longest edge length to shortest edge length