Sample Problems > Usage > 3D_domains > 3d

{ 3D_PYRAMID.PDE

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

It demonstrates the use of FlexPDE in 3D problems with non-planar

extrusion surfaces.

Note that FEATURE paths are used to delineate discontinuities in the

extrusion surfaces.

The outer edge is used as a heat source, so it is clipped to form an edge wall.

}

title '3D Test - Pyramid'

coordinates

cartesian3

select

regrid=off

ngrid=5 { reduce mesh size for example }

variables

definitions

k = 0.1

heat = 4

equations

U: div(K*grad(u)) + heat = 0

extrusion

surface z = 0

surface z = min(1.1- abs(x),1.1-abs(y))

boundaries

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

Region 1

start(-1,-1)

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

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

{ Features delineate hidden discontinuities in surface slope.

This forces gridding nodes along break lines. }

feature start(-1,-1) line to (1,1)

feature start(-1,1) line to (1,-1)

plots

contour(u) on x=0 as "YZ plane intersects peak"

contour(u) on y=0 as "XZ plane intersects peak"

contour(u) on z=0.1 as "XY plane intersects full outline"

contour(u) on x=0.51 as "YZ plane near midpoint of side slope"

contour(u) on x+y=0.51 as "Oblique plane cuts corner"

contour(u) on z=0.8 as "XY plane near tip"

contour(u) on z=0.8 zoom as "XY plane near tip - zoomed"

end

3d_pyramid