﻿ Sample Problems > Usage > 3D_domains > 3d_spherebox

# 3d_spherebox

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# 3d_spherebox   { 3D_SPHEREBOX.PDE

An empty 3D sphere inside a box.

}

title 'Empty 3D Sphere in a box'

coordinates

cartesian3

variables

u

definitions

K = 0.1                     { conductivity }

R0 = 1                     { radius }

box = 2*R0

zsphere = SPHERE ((0,0,0),R0)   {  hemisphere shape }

equations

extrusion

surface z=-box

surface z = -zsphere       { the bottom hemisphere and plane }

surface z = zsphere         { the top hemisphere and plane }

surface z=box

boundaries

surface 1 value(u) = 0     { fixed value on box surfaces }

surface 4 value(u) = 1

Region 1       { the bounding box - defaults to insulating sidewalls }

start(-box,-box)

line to (box,-box) to (box,box) to (-box,box) to close

Limited Region 2           { sphere exists only in region 2 }

layer 2 void           { ... and layer 2 }

start  (R0,0)

arc(center=0,0) angle=360

plots

grid(x,y,z)

grid(x,z) on y=0

contour(u) on x=0

end