{ 3D_LIMITED_REGION.PDE
This example shows the use of LIMITED REGIONS in 3D applications.
The LIMITED qualifier applied to a REGION section tells FlexPDE to construct
the region only in those layers or surfaces specifically referenced in the region
definition.
In this problem, we have a heat equation with a small cubical heated box in the middle layer.
}
title '3D LIMITED REGION TEST'
coordinates
cartesian3
select
errlim = 0.005
ngrid=1 { exaggerate cell size disparity }
Variables
u
definitions
k = 0.1
h=0
Lx=3 Ly=3 Lz=3
w = 0.15 { box size }
x0=Lx/2-w y0=Ly/2-w z0=Lz/2-w { box coords }
x1=Lx/2+w y1=Ly/2+w z1=Lz/2+w
equations
div(K*grad(u)) + h = 0
extrusion z=0, z0, z1, Lz
boundaries
Region 1
start(0,y0)
value(u)=0
line to (Lx,y0) to (Lx,Ly) to (0,Ly) to close
limited region 2 { insert exists only on layer 2 }
layer 2 K=9 h=1
start(x0,y0)
line to (x1,y0) to (x1,y1) to (x0,y1) to close
monitors
grid(x,z) on y=Ly/2
contour(u) on z=Lz/2
plots
grid(x,z) on y=Ly/2
contour(u) on z=Lz/2 painted
contour(u) on y=Ly/2 painted
end