3d_lenses

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3d_lenses

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{ 3D_LENSES.PDE

 

 This problem considers the flow of heat in a lens-shaped body

 of square outline.  It demonstrates the use of FlexPDE in problems

 with non-planar extrusion surfaces.

 

 Layer 1 consists of a flat bottom with a paraboloidal top.

 Layer 2 is a paraboloidal sheet of uniform thickness.

 

 Plots on various cut planes show the ability of FlexPDE to

 detect intersection surfaces.

 

}  

 

title '3D Test - Lenses'  

 

coordinates  

    cartesian3  

 

Variables  

    u  

 

definitions  

    k = 0.1  

    heat = 4  

 

equations  

   U: div(K*grad(u)) + heat   = 0  

 

extrusion  

  surface z = 0  

  surface z = 0.8-0.3*(x^2+y^2)  

  surface z = 1.0-0.3*(x^2+y^2)  

 

 

boundaries  

    { implicit natural(u) = 0 on top and bottom faces }  

    Region 1  

      layer 2 k = 1   { layer specializations must follow regional defaults }  

      start(-1,-1)  

      value(u) = 0     { Fixed value on sides }  

      line to (1,-1) to (1,1) to (-1,1) to close  

 

select painted  

plots  

    contour(u) on x=0.51       as "YZ plane"  

    contour(u) on y=0.51       as "XZ plane"  

    contour(u) on z=0.51       as "XY plane cuts both layers and part of outline"  

    contour(u) on z=0.75       as "XY plane cuts both layers, but not the outline"  

    contour(u) on z=0.8       as "XY plane cuts only layer 2"  

    contour(u) on z=0.95       as "XY plane cuts small patch of layer 2"  

    contour(u) on z=0.95 zoom as "small cut patch, zoomed to fill frame"  

    contour(u) on surface 1   as "on bottom surface"  

    contour(u) on surface 2   as "on paraboloidal layer interface"  

    contour(u) on x=y         as "oblique plot plane"  

    contour(u) on x+y=0       as "another oblique plot plane"  

 

end