POLAR COORDINATES

 

Any grid specified using the PHOENICSgrid file must be a BFC type grid and therefore must always be topologically cartesian. However, if a cylindrical polar grid is required this can be achieved by giving a number of cell corners the same coordinates. The elements thus generated are 8 noded bricks degenerated to be 6 noded wedges. This can be achieved in FEMGEN using the method illustrated by the following example.

In 2D a polar grid has triangular cells at its centre. These cells can also be defined as quadrilaterals with two corners at the same point. To generate such elements, a four sided surface must be generated with one side of zero length. To conform with FEMGEN geometry rules this side must have distinct points at each end so TWO coincident points must be defined, and number of 'divisions' along the zero length line must be the same as those along the line on the opposite side of the surface.

To generate a second surface another point must be generated coincident with the first two points. It is easier if you imagine the lines generated to be very short and then make the surfaces and bodies generated conform to the rules defined above. In two dimensions a typical cylindrical mesh would be as shown in Figure 3.1. The lengths of lines L1, L2, L3 and L4 have been increased from zero to show the model structure.

 

Figure 3.1: An Exploded View of a Cylindrical Mesh

If you wish to transform a surface or body with coincident points, the tolerance used to test for coincident points in FEMGENmust first be set to zero using the command :-

CONSTRUCT SPACE TOLERANCE 0

This will prevent coincident points being merged and the geometry definition failing.