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{ 3D_SPHEREBOX.PDE

 

 An empty 3D sphere inside a box.

}  

 

title 'Empty 3D Sphere in a box'  

 

coordinates  

   cartesian3  

 

variables  

   u  

 

definitions  

   K = 0.1                     { conductivity }  

   R0 = 1                     { radius }  

   box = 2*R0  

 

   zsphere = SPHERE ((0,0,0),R0)   {  hemisphere shape }  

 

equations  

   U: div(K*grad(u))    = 0  

 

extrusion  

  surface z=-box  

  surface z = -zsphere       { the bottom hemisphere and plane }  

  surface z = zsphere         { the top hemisphere and plane }  

  surface z=box  

 

boundaries  

  surface 1 value(u) = 0     { fixed value on box surfaces }  

  surface 4 value(u) = 1  

 

  Region 1       { the bounding box - defaults to insulating sidewalls }  

      start(-box,-box)  

      line to (box,-box) to (box,box) to (-box,box) to close  

 

  Limited Region 2           { sphere exists only in region 2 }  

      layer 2 void           { ... and layer 2 }  

      start  (R0,0)  

          arc(center=0,0) angle=360  

 

plots  

  grid(x,y,z)  

  grid(x,z) on y=0  

  contour(u) on x=0  

  glcontour(u)

 

end