3d_limited_region

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3d_limited_region

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{ 3D_LIMITED_REGION.PDE  

 

 This example shows the use of LIMITED REGIONS in 3D applications.

 

 The LIMITED qualifier applied to a REGION section tells FlexPDE to construct

 the region only in those layers or surfaces specifically referenced in the region

 definition.

 

 In this problem, we have a heat equation with a small cubical heated box in the middle layer.

 

}  

 

title '3D LIMITED REGION TEST'  

 

coordinates

   cartesian3  

 

select

   ngrid=1 { exaggerate cell size disparity }  

 

variables

   u  

 

definitions  

   K = 0.1  

   h=0  

   Lx=3    Ly=3  Lz=3  

   w = 0.15       { box size }  

   x0=Lx/2-w  y0=Ly/2-w  z0=Lz/2-w { box coords }  

   x1=Lx/2+w  y1=Ly/2+w  z1=Lz/2+w  

 

materials 'insert' : K=9 h=1

 

equations  

   U:  div(K*grad(u)) + h = 0  

 

extrusion z=0, z0, z1, Lz  

 

boundaries  

  Region 1  

    start(0,y0)  

    value(u)=0              

    line to (Lx,y0) to (Lx,Ly) to (0,Ly) to close  

 

  limited region 2       { insert exists only on layer 2 }  

    layer 2 use material 'insert'  

    start(x0,y0)  

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

 

monitors  

  grid(x,z) on y=Ly/2  

  contour(u) on z=Lz/2  

 

plots  

  grid(x,z) on y=Ly/2  

  contour(u) on z=Lz/2  painted  

  contour(u) on y=Ly/2  painted  

 

end