A Cylindrical Example

A Cylindrical Example

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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 }

Rad = 0.5 { blob radius (renamed)}

EQUATIONS

Div(-k*grad(phi)) = 0

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

START 'ring' (1,Rad)

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

PLOTS

CONTOUR(Phi)

VECTOR(-k*grad(Phi))

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

ELEVATION(Normal(-k*grad(Phi))) ON 'ring'

END

The resulting contour and boundary plot look like this: