{
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
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
plots
contour(u) on x=0.51 { YZ plane }
contour(u) on y=0.51 { XZ plane }
contour(u) on z=0.51 { XY plane intersects both layers and part of domain boundary }
contour(u) on z=0.75 { XY plane intersects both layers, but not th outline }
contour(u) on z=0.8 { XY plane intersects only layer 2 }
contour(u) on z=0.95 { XY plane intersects smaller patch of layer 2 }
contour(u) on z=0.95 zoom { previous plot, zoomed to fill frame }
contour(u) on surface 1 { on bottom surface }
contour(u) on surface 2 { on paraboloidal layer interface }
contour(u) on x=y { oblique plot plane }
contour(u) on x+y=0 { another oblique plot plane }
end