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# A Cylindrical Example

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# A Cylindrical Example   Let us now convert our Cartesian test problem into a cylindrical one.  If we rotate the box and blob around the left boundary, we will form a torus between two circular plates (like a donut in a round box).

These changes will be required:

 • We must offset the coordinates, so the left boundary becomes R=0.
 • Since we want the rotation axis in the Y-direction, we must use YCYLINDER coordinates.
 • Since 'R' is now a coordinate name, we must rename the 'R' used for the blob radius.

The full script, converted to cylindrical coordinates is then:

TITLE 'Heat flow around an Insulating Torus'

COORDINATES

YCYLINDER

VARIABLES

Phi                { the temperature }

DEFINITIONS

K = 1                { default conductivity }

EQUATIONS

BOUNDARIES

REGION 1 'box'

START(0,-1)

VALUE(Phi)=0        LINE TO (2,-1)

NATURAL(Phi)=0        LINE TO (2,1)

VALUE(Phi)=1        LINE TO (0,1)

NATURAL(Phi)=0        LINE TO CLOSE

REGION 2        'blob'        { the embedded blob }

k = 0.001

ARC(CENTER=1,0) ANGLE=360 TO CLOSE

PLOTS

CONTOUR(Phi)

ELEVATION(Phi) FROM (1,-1) to (1,1)

END

The resulting contour and boundary plot look like this:  