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# 2d_blob_velocity

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# 2d_blob_velocity

{ 2D_BLOB_VELOCITY.PDE

This problem illustrates moving meshes in 2D.

A circular boundary shrinks and grows sinusoidally in time.

The mesh coordinates are solved by reference to a mesh velocity variable.

See 2D_BLOB_POSITION.PDE for a version that uses no mesh velocity variables.

}

TITLE 'Pulsating circle in 2D - velocity specification'

COORDINATES

cartesian2

VARIABLES

Phi           { the temperature }

Xm = MOVE(x) { surrogate X }

Ym = MOVE(y) { surrogate Y }

Um(0.1)       { mesh x-velocity }

Vm(0.1)       { mesh y-velocity }

DEFINITIONS

K = 1   { default conductivity }

R0 = 0.75   { initial blob radius }

INITIAL VALUES

Phi = (y+1)/2

EULERIAN EQUATIONS

Xm:  dt(Xm) = Um

Ym:  dt(Ym) = Vm

BOUNDARIES

REGION 1 'box'

START(-1,-1)

VALUE(Phi)=0

VELOCITY(Xm)=0 VELOCITY(Ym)=0

VALUE(Um)=0 VALUE(Vm)=0

LINE TO (1,-1)

NATURAL(Phi)=0

LINE TO (1,1)

VALUE(Phi)=1

LINE TO (-1,1)

NATURAL(Phi)=0

LINE TO CLOSE

REGION 2 'blob' { the embedded blob }

k = 0.001

START 'ring' (R0,0)

VELOCITY(Xm) = Um

VELOCITY(Ym) = Vm

VALUE(Um) = -0.25*sin(t)*x/r

VALUE(Vm) = -0.25*sin(t)*y/r

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

TIME 0 TO 2*pi

MONITORS

for cycle=1

grid(x,y)

contour(phi)

PLOTS

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

GRID(x,y)

CONTOUR(Phi)  notags nominmax

CONTOUR(magnitude(Um,Vm))

VECTOR(Um,Vm) fixed range(0,0.25)

ELEVATION(Phi) FROM (0,-1) to (0,1)

END