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# 3d_blob_position

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# 3d_blob_position

{ 3D_BLOB_POSITION.PDE

This problem illustrates moving meshes in 3D.

A spherical boundary shrinks and grows sinusoidally in time.

The mesh coordinates are solved directly, without a mesh velocity variable.

See 3D_BLOB_VELOCITY.PDE for a version that uses mesh velocity variables.

}

TITLE 'Pulsating circle in 3D - position specification'

COORDINATES

cartesian3

VARIABLES

Phi   { the temperature }

Xm = MOVE(x) { surrogate X }

Ym = MOVE(y) { surrogate Y }

Zm = MOVE(z) { surrogate Z }

DEFINITIONS

K = 1   { default conductivity }

R0 = 0.75   { initial blob radius }

zsphere = SPHERE ((0,0,0),R0)

z1, z2

Um = dt(Xm)

Vm = dt(Ym)

Wm = dt(Zm)

INITIAL VALUES

Phi = (z+1)/2

EULERIAN EQUATIONS

Phi:  Div(-k*grad(phi)) = 0

Xm:  div(grad(Xm)) = 0

Ym:  div(grad(Ym)) = 0

Zm:  div(grad(Zm)) = 0

EXTRUSION

SURFACE 'Bottom'          z = -1

SURFACE 'Sphere Bottom'   z=z1

SURFACE 'Sphere Top'      z=z2

SURFACE 'Top'             z=1

BOUNDARIES

SURFACE 1

VALUE(Phi)=0 VELOCITY(Xm)=0 VELOCITY(Ym)=0 VELOCITY(Zm)=0

SURFACE 4

VALUE(Phi)=1 VELOCITY(Xm)=0 VELOCITY(Ym)=0 VELOCITY(Zm)=0

REGION 1 'box'

z1=0   z2=0

START(-1,-1)

NATURAL(Phi)=0 VELOCITY(Xm)=0 VELOCITY(Ym)=0 VELOCITY(Zm)=0

LINE TO (1,-1) TO (1,1) TO (-1,1) TO CLOSE

LIMITED REGION 2 'blob' { the embedded blob }

z1 = -zsphere

z2 = zsphere

layer 2 k = 0.001

SURFACE 2

VELOCITY(Xm) = -0.25*sin(t)*x/r

VELOCITY(Ym) = -0.25*sin(t)*y/r

VELOCITY(Zm) = -0.25*sin(t)*z/r

SURFACE 3

VELOCITY(Xm) = -0.25*sin(t)*x/r

VELOCITY(Ym) = -0.25*sin(t)*y/r

VELOCITY(Zm) = -0.25*sin(t)*z/r

START 'ring' (R0,0)

ARC(CENTER=0,0) ANGLE=360 TO CLOSE

TIME 0 TO 2*pi by pi/20

MONITORS

FOR cycle=1

GRID(x,y,z) ON 'blob' ON LAYER 2

CONTOUR(phi) ON y=0

PLOTS

FOR T = 0 BY pi/20 TO 2*pi

GRID(x,y,z) ON 'blob' ON LAYER 2 FRAME(-R0,-R0,-R0, 2*R0,2*R0,2*R0)

CONTOUR(Phi)  notags nominmax ON y=0