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{ 3D_BUBBLE_RECONNECT.PDE
This problem illustrates moving meshes and mesh reconnection in 3D.
A spherical bubble moves through a column.
A mesh velocity variable is used to compute the mesh coordinates.
}
TITLE '3D Bubble reconnect - velocity specification'
SELECT overshoot = 1e-5 reconnect(on) order=2
COORDINATES cartesian3
VARIABLES Phi(0.001) { the temperature } Zm = MOVE(z) { surrogate Z variable} Wm(0.01) { mesh z-velocity }
DEFINITIONS K = 1 { default conductivity } Vz = 0.1 length=5
zc = 1 ! bubble center R0 = 0.5 { bubble radius } zsphere = SPHERE ((0,0,0),R0) z1, z2 km =100
INITIAL VALUES Phi = 0 Wm=0
INITIAL EQUATIONS Phi: Div(-k*grad(phi)) = 0 Wm: div(km*grad(Wm)) = 0
EULERIAN EQUATIONS Phi: Div(k*grad(phi)) = dt(phi) Zm: dt(Zm) = Wm Wm: div(km*grad(Wm)) = 0
EXTRUSION SURFACE 'Bottom' z = 0 SURFACE 'Sphere Bottom' z=zc-zsphere layer "zbubble" SURFACE 'Sphere Top' z=zc+zsphere SURFACE 'Top' z=length
BOUNDARIES
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SURFACE 1
VALUE(Phi)=0 VELOCITY(Zm)=0 VALUE(Wm)=0
SURFACE 2
VALUE(Wm) = Vz
VELOCITY(Zm) = Vz
SURFACE 3
VALUE(Wm) = Vz
VELOCITY(Zm) = Vz
SURFACE 4
VALUE(Phi)=0 VELOCITY(Zm)=0 VALUE(Wm)=0
REGION 1 'box'
z1=0 z2=0
START(1,0)
VALUE(Phi)=0
natural(Wm)=0
LINE TO (1,1) TO (-1,1) TO(-1,0)
NATURAL(Phi)=0
NATURAL(Wm)=0
NOBC(Zm)
LINE TO CLOSE
LIMITED
REGION 2 'bubble' { the embedded bubble }
z1 = zc-zsphere
z2 = zc+zsphere
layer "zbubble"
k = 0.001
mesh_spacing = 0.25
SURFACE 'Sphere Bottom'
VELOCITY(Zm) = Wm
VALUE(Wm) = Vz
value(phi)=1
SURFACE 'Sphere Top'
VELOCITY(Zm) = Wm
VALUE(Wm) = Vz
value(phi)=1
start(R0,0) arc(center=0,0) angle=180
natural(Wm)=0 line to close
TIME 0 TO 30 by 0.1
PLOTS
for t=0
GRID(x,y,z) ON 'bubble' ON LAYER "zbubble"
for cycle=1
grid(X,Z) on y=0 paintregions
grid(X,Y) on surface 'Sphere Bottom'
grid(Y,Z) on x=0.33
CONTOUR(Wm) notags nominmax ON y=0 as "Mesh Velocity"
CONTOUR(dt(Wm)) notags nominmax ON y=0 as "Mesh Acceleration"
CONTOUR(phi) notags nominmax ON y=0
CONTOUR(dt(phi)) notags nominmax ON y=0
glcontour(Wm) on region 1 on layer 1
END
