3d_bubble_reconnect

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3d_bubble_reconnect

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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

 

 

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