Cylindrical Geometry

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Cylindrical Geometry

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In addition to two-dimensional Cartesian geometry, FlexPDE can solve problems in axisymmetric cylindrical coordinates, (r,z) or (z,r).

Cylindrical coordinates are invoked in the COORDINATES section of the script.  Two forms are available, XCYLINDER and YCYLINDER.  The distinction between the two is merely in the orientation of the graphical displays.

XCYLINDER places the rotation axis of the cylinder, the Z coordinate, along the abscissa (or "x"-axis) of the plot, with radius along the ordinate.  Coordinates in this system are (Z,R)
YCYLINDER places the rotation axis of the cylinder, the Z coordinate, along the ordinate (or "y" axis) of the plot, with radial  position along the abscissa.  Coordinates in this system are (R,Z)

 

Either form may optionally be followed by a parenthesized renaming of the coordinates.  Renaming cannot be used to change the geometric character of the coordinate.  Radius remains radius, even if you rename it "Z".

The default names are

XCYLINDER  implies XCYLINDER('Z','R').

YCYLINDER  implies YCYLINDER('R','Z').