sine3d

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sine3d

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{ SINE3D.PDE

   

 This problem compares the solution accuracy for three different levels of ERRLIM.  

 

}  

 

title '3D Accuracy Test - Sine'

 

coordinates

   cartesian3

 

select

   ngrid = 5

   errlim = staged(1e-2, 3e-3, 1e-3, 3e-4, 1e-4)

 

variables

   u

 

definitions

   long = 1

   wide = 1

   z1 = -1

   z2 = 1

   w=0.1

   rs = r/w

   uex = sin(rs)/rs

   s = -(dxx(uex)+dyy(uex)+dzz(uex))

   RMS_error = sqrt(integral((u-uex)^2)/sqrt(integral(uex^2)))

 

equations

   U:    div(grad(u)) + s = 0

 

extrusion z = z1,z2

 

boundaries

  surface 1 value(u)=uex     { fix bottom surface temp }

  surface 2 value(u)=uex     { fix top surface temp }

 

  Region 1               { define full domain boundary in base plane }

      start(-wide,-wide)

        value(u) = uex         { fix all side temps }

        line to (wide,-wide)   { walk outer boundary in base plane }

          to (wide,wide)

          to (-wide,wide)

          to close

 

monitors

  grid(x,z) on y=0 as "Grid on X-Z cut"

  contour(uex) on y=0 as "Exact Solution Uex"

  contour(u) on y=0 as "Numerical Solution U"

  contour(u-uex) on y=0 as "Actual error U-Uex"

 

plots

  grid(x,z) on y=0 as "Grid on X-Z cut"

  contour(uex) on y=0 as "Exact Solution Uex"

  contour(u) on y=0 as "Numerical Solution U"

  contour(u-uex) on y=0 as "Actual error U-Uex"

  summary

      report(errlim) as "Requested error"

      report(RMS_error)

 

histories

  history(RMS_error, errlim) LOG

 

 

end