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# azimuthal_periodic

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# azimuthal_periodic

{  AZIMUTHAL_PERIODIC.PDE

This example shows the use of FlexPDE in a problem with azimuthal periodicity.

(See the example PERIODIC.PDE for notes on periodic boundaries.)

In this problem we create a repeated 45-degree segment of a ring.

}

 title 'AZIMUTHAL PERIODIC TEST' Variables    u definitions    k = 1   { angular size of the repeated segment: }    an = pi/4       { the sine and cosine for transformation }    crot = cos(an)      srot = sin(an)    H = 0    xc = 1.5    yc = 0.2    rc = 0.1 equations    u : div(K*grad(u)) + H = 0 boundaries   region 1

{ this line forms the remote boundary for the later periodic statement }

start(1,0) line to (2,0)

value(u)=0 arc(center=0,0) to (2*crot,2*srot)

{ The following line segment is periodic under an angular rotation.

The mapping expressions take each point on the line into a corresponding

point in the base line.  Note that although all the mapped y-coordinates

will be zero, we give the general expression so that the transformation

will be invertible. }

periodic(x*crot+y*srot, -x*srot+y*crot)

line to (crot,srot)

value(u)=0

arc(center= 0,0) to close

region 2

H = 1

start(xc-rc,yc) arc(center=xc,yc) angle=360

monitors

grid(x,y)

contour(u)

plots

grid(x,y) contour(u)

end