3d_pyramid

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3d_pyramid

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{ 3D_PYRAMID.PDE

 

 This problem considers the flow of heat in a pyramid-shaped body.

 It demonstrates the use of FlexPDE in 3D problems with non-planar

 extrusion surfaces.

 

 Note that FEATURE paths are used to delineate discontinuities in the

 extrusion surfaces.

 

 The outer edge is used as a heat source, so it is clipped to form an edge wall.  

 

 

}  

 

title '3D Test - Pyramid'  

 

coordinates

   cartesian3  

 

select  

   regrid=off  

   ngrid=5 { reduce mesh size for example }

 

variables

   u  

 

definitions  

   k = 0.1  

   heat = 4  

 

equations  

   U: div(K*grad(u)) + heat   = 0  

 

extrusion  

  surface z = 0  

  surface z = min(1.1- abs(x),1.1-abs(y))  

 

 

boundaries  

    { implicit natural(u) = 0 on top and bottom faces }  

  Region 1  

      start(-1,-1)  

      value(u) = 0           { Fixed value on short vertical sides }  

          line to (1,-1) to (1,1) to (-1,1) to close  

 

  { Features delineate hidden discontinuities in surface slope.

     This forces gridding nodes along break lines. }  

  feature start(-1,-1) line to (1,1)  

  feature start(-1,1) line to (1,-1)  

 

plots  

  contour(u) on x=0         as "YZ plane intersects peak"  

  contour(u) on y=0         as "XZ plane intersects peak"  

  contour(u) on z=0.1       as "XY plane intersects full outline"  

  contour(u) on x=0.51       as "YZ plane near midpoint of side slope"  

  contour(u) on x+y=0.51     as "Oblique plane cuts corner"  

  contour(u) on z=0.8       as "XY plane near tip"  

  contour(u) on z=0.8 zoom as "XY plane near tip - zoomed"  

 

end