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<< Click to Display Table of Contents >> 3d_torus |
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{ 3D_TORUS.PDE
This problem constructs a torus.
The top surface and bottom surface meet along the diameter of the torus.
}
title '3D Torus'
coordinates
cartesian3
select
errlim = 0.005
ngrid = 20 { get better mesh resolution of curved surfaces }
painted
variables
u
definitions
Raxis = 4 { the radius of the toroid axis }
Rtube = 1 { the radius of the toroid tube }
Rad = sqrt(x^2+y^2) { cylindrical radius of point (x,y) }
{ the torus surface is the locus of points where (Rad-Raxis)^2+Z^2 = Rtube^2 }
ZTorus = sqrt(Rtube^2-(Rad-Raxis)^2)
equations U: del2(u) + 1 = 0
extrusion Surface "Bottom" z = -ZTorus Surface "Top" z = ZTorus
boundaries surface 1 value(u)=0 surface 2 value(u) = 0
region 1 start(Raxis+Rtube, 0) value(u) = 0 |
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arc(center=0,0) angle=360 { the outer boundary }
start(Raxis-Rtube, 0)
value(u) = 0
arc(center=0,0) angle=360 { the inner boundary }
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
