3d_zperiodic

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3d_zperiodic

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{  3D_ZPERIODIC.PDE

 

 This example shows the use of FlexPDE in 3D applications with periodic

 boundaries in the Z-direction.

 

 For Z-periodicity, we merely precede  the EXTRUSION statement by the

 qualifier PERIODIC.  The top and bottom surfaces are assumed to match,

 and values are made equal on the two surfaces.

 

 In this problem we have a heat equation in an irregular figure.

 An off-center source heats the body, while all the vertical surfaces are

 held at U=0.

 

}  

 

title '3D Z-PERIODIC BOUNDARY TEST'  

 

coordinates  

   cartesian3  

 

Variables  

    u  

 

definitions  

   k = 0.1  

   h=0  

   x0=0.3  y0=-0.2  

   x1=0.7  y1 = 0.2  

 

equations  

   u : div(K*grad(u)) + h = 0  

 

periodic extrusion z=0, 0.8, 1  

 

boundaries  

  Region 1  

    start(-1,-1)  

      value(u)=0  

    line to (1,-1)  

    arc(center=-1,0) to (1,1)  

    line to (-1,1)  

    arc(center=-3,0) to close  

 

 

 

 

 

  { an off-center heat source in layer 2 provides the asymmetric

       conditions to demonstrate the periodicity of the solution }  

  limited region 2  

    layer 2 h=10 k=10  

    surface 1 { include insert patch in surface 1 so surfaces match }  

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

 

monitors  

  contour(u) on y=0  

 

plots  

  grid(x,z) on y=0  

  contour(u) on y=0 painted  

end