periodic+time

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periodic+time

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{ PERIODIC+TIME.PDE

 

 This example is a time-dependent version of PERIODIC.PDE

 

}  

 

title 'Time-dependent Periodic Boundary Test'  

 

variables  

    u(0.01)  

 

definitions  

   k = 0.1  

   h=0  

   x0=0.5  y0=-0.2  

   x1=1.1  y1=0.2  

 

equations  

   u : div(K*grad(u)) + h = dt(u)  

 

boundaries  

  region 1  

    start(-1,-1)  

    value(u)=0 line to (0.9,-1) to (1,-1)  

 

    { The following arc is required to be a periodic image of an arc

       two units to its left. (This image boundary has not yet been defined.) }  

    periodic(x-2,y) arc(center=-1,0) to (1,1)  

 

    value(u)=0   line to (-1,1)  

 

    { The following arc provides the required image boundary for the previous

       periodic statement }  

    nobc(u)   { turn off the value BC }  

    arc(center= -3,0) to close  

 

  { an off-center heat source provides the asymmetric conditions to

     demonstrate the periodicity of the solution }  

  region 2  h=10 k=10  

    start(x0,y0) line to (x1,y0) to (x1,y1) to (x0,y1) to close  

 

time 0 to 10  

 

monitors  

  for cycle=1  

    grid(x,y)  

    contour(u)  

 

plots  

  for cycle=10  

    grid(x,y)  

    contour(u)  

 

end