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