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The Pulsating Blob
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| TITLE 'Heat flow around an Insulating blob'
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| VARIABLES
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| Phi { the temperature }
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| Xm = MOVE(x) { surrogate X }
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| Ym = MOVE(y) { surrogate Y }
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| DEFINITIONS
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| K = 1 { default conductivity }
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| R0 = 0.75 { initial blob radius }
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| EQUATIONS
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| Phi: Div(-k*grad(phi)) = 0
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| Xm: div(grad(Xm)) = 0
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| Ym: div(grad(Ym)) = 0
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| BOUNDARIES
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| REGION 1 'box'
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| START(-1,-1)
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| VALUE(Phi)=0
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| VELOCITY(Xm)=0 VELOCITY(Ym)=0
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| LINE TO (1,-1)
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| NATURAL(Phi)=0
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| LINE TO (1,1)
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| VALUE(Phi)=1
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| LINE TO (-1,1)
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| NATURAL(Phi)=0
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| LINE TO CLOSE
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| REGION 2 'blob' { the embedded blob }
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| k = 0.001
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| START 'ring' (R,0)
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| VELOCITY(Xm) = -0.25*sin(t)*x/r
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| VELOCITY(Ym) = -0.25*sin(t)*y/r
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| ARC(CENTER=0,0) ANGLE=360 TO CLOSE
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| PLOTS
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| TIME 0 TO 2*pi
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| PLOTS
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| FOR T = pi/2 BY pi/2 TO 2*pi
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| GRID(x,y)
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| CONTOUR(Phi)
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| VECTOR(-k*grad(Phi))
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| ELEVATION(Phi) FROM (0,-1) to (0,1)
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| ELEVATION(Normal(-k*grad(Phi))) ON 'ring'
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| END
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