<< Click to Display Table of Contents >> 3d_lenses 

{ 3D_LENSES.PDE
This problem considers the flow of heat in a lensshaped body
of square outline. It demonstrates the use of FlexPDE in problems
with nonplanar 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 = 0.80.3*(x^2+y^2) surface z = 1.00.3*(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