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{ 3D_TORUS_TUBE.PDE
This problem constructs a "U" of pipe by connecting two cylindrical stubs to the
ends of a 180-degree arc of a torus.
There are three layers:
1) the bottom half of the outer pipe
2) the inner fluid
3) the top half of the outer pipe.
Layers 1 and 3 wrap around layer 3 and meet on the center plane.
There are six regions, the inside and outside parts of the torus and the two stubs.
}
title '3D Torus Tube'
coordinates
cartesian3
select
errlim = 0.005
painted
variables
u
definitions
Ra = 4 { the radius of the toroid axis }
Rt = 1 { the radius of the outer toroid }
Ri = 0.6 { the radius of the inner toroid }
Len = 3 { the length of the side tubes }
{ Surface Definitions - Toroids and Tubes}
Rad = sqrt(x^2+y^2)
ZTorus1 = sqrt(Rt^2-(Rad-Ra)^2) ! outside toroid
ZTorus2 = sqrt(Ri^2-(Rad-Ra)^2) ! inside toroid
ZTube1a = CYLINDER ((Ra,0,0), (Ra,1,0), Rt) ! outside tube A
ZTube1b = CYLINDER ((-Ra,0,0), (-Ra,1,0), Rt) ! outside tube B
ZTube2a = CYLINDER ((Ra,0,0), (Ra,1,0), Ri) ! inside tube A
ZTube2b = CYLINDER ((-Ra,0,0), (-Ra,1,0), Ri) ! inside tube B
{ Surface Definitions - default values for region 1 }
z1 = -ZTorus1
z2 = 0
z3 = 0
z4 = ZTorus1
{ heat source and conductivity }
s = 1
k = 1
equations
u: div(k*grad(u)) + s = 0
extrusion
Surface "Bottom1" z = z1
Surface "Bottom2" z = z2
Surface "Top2" z = z3
Surface "Top1" z = z4
boundaries
surface "Bottom1" value(u)=0
surface "Top1" value(u) = 0
region 1 "Outside Toroid"
mesh_spacing = Rt/2
layer 1 s = 1 k = 10
layer 3 s = 1 k = 10
start(Ra+Rt, 0)
value(u) = 0
arc(center=0,0) angle=180 { the outer boundary }
natural(u) = 0
line to (-Ra+Rt, 0)
value(u) = 0
arc(center=0,0) angle=-180 { the inner boundary }
natural(u) = 0
line to close
limited region 2 "Inside Toroid"
z2 = -ZTorus2
z3 = ZTorus2
mesh_spacing = Ri/2
layer 2 s = 100 k = 1
start(Ra+Ri, 0)
arc(center=0,0) angle=180 { the outer boundary }
line to (-Ra+Ri, 0)
arc(center=0,0) angle=-180 { the inner boundary }
line to close
region 3 "Outside TubeA"
z1 = -ZTube1a
z4 = ZTube1a
mesh_spacing = Rt/2
layer 1 s = 1 k = 10
layer 3 s = 1 k = 10
start (Ra+Rt,0)
line to (Ra+Rt,-Len)
line to (Ra-Rt,-Len)
line to (Ra-Rt,0)
line to close
limited region 4 "Inside TubeA"
z1 = -ZTube1a
z2 = -ZTube2a
z3 = ZTube2a
z4 = ZTube1a
mesh_spacing = Ri/2
layer 2 s = 100 k = 1
start (Ra+Ri,0)
line to (Ra+Ri,-Len)
line to (Ra-Ri,-Len)
line to (Ra-Ri,0)
line to close
region 5 "Outside TubeB"
z1 = -ZTube1b
z4 = ZTube1b
mesh_spacing = Rt/2
layer 1 s = 1 k = 10
layer 3 s = 1 k = 10
start (-Ra-Rt,0)
line to (-Ra-Rt,-Len)
line to (-Ra+Rt,-Len)
line to (-Ra+Rt,0)
line to close
limited region 6 "Inside TubeB"
z2 = -ZTube2b
z3 = ZTube2b
mesh_spacing = Ri/2
layer 2 s = 100 k = 1
start (-Ra-Ri,0)
line to (-Ra-Ri,-Len)
line to (-Ra+Ri,-Len)
line to (-Ra+Ri,0)
line to close
monitors
grid(x,y,z)
contour(u) on surface z=0
contour(u) on surface y=0
plots
grid(x,y,z)
contour(u) on surface z=0
contour(u) on surface y=0
end