Sample Problems > Usage > 3D_domains > 3d

{ 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

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

3d_lenses