KENO Shannon Entropy Test 1 for infinite lattice

[Paul Smith]

I'm running infinite lattice calculations using KENO-V.a.  The fuel type is PWR 17x17.  I find that no matter what I use for the nsk, gen, and npg parameters, I will always fail Test 1 of the source convergence tests.  For instance, with gen=4500, npg=6000, and nsk=500, I get the following for Test 1 source convergence test results:

 --------------------------------------------------------------------------------------------|----------------

  Test 1: Is the final fission source converged?                                             | Test 1: failed

 --------------------------------------------------------------------------------------------|----------------

 Test 1 details:

 Is the mean square posterior relative entropy <  the center mean square Shannon entropy?

  ( msq(D) < cmsq(H(S)) )

 generations skipped     msq         cmsq

                 500  2.97240E-04  1.05226E-05

                 700  2.97823E-04  1.05782E-05

                 900  2.98156E-04  1.06247E-05

                1100  2.97618E-04  1.06409E-05

                1300  2.97593E-04  1.05987E-05

                1500  2.98143E-04  1.05921E-05

                1700  2.99638E-04  1.04781E-05

                1900  3.01117E-04  1.04937E-05

                2100  3.01698E-04  1.06591E-05

                2300  3.01876E-04  1.08293E-05

                2500  3.01826E-04  1.09230E-05

                2700  3.00674E-04  1.06824E-05

                2900  2.99201E-04  1.05194E-05

                3100  2.98848E-04  1.02020E-05

                3300  2.99254E-04  1.02661E-05

                3500  2.98456E-04  1.02209E-05

                3700  2.97526E-04  1.02516E-05

                3900  3.00541E-04  1.03935E-05

                4100  3.04216E-04  1.06059E-05

                4300  3.12479E-04  7.64459E-06

I've tried running a ridiculous number of particles per generation and skipping more particles, but the results are always nearly the same.  This isn't surprising though considering that the msq and cmsq values are barely changing in this example.

The issue I have found is that the test seems to fail when the source distribution is nearly constant across all bins.  I first tested this with a simple Excel spreadsheet where I model a uniform source distribution with random perturbations of a size that I can adjust.  I also tried the same spreadsheet with a peaked distribution.  I see that the peaked distribution passes the test for reasonable perturbations (~10%) but the uniform distribution fails for any perturbation that is greater than roughly 1e-12 at which point I assume machine precision limits the calculation accuracy.  See attached spreadsheet.

Because I'm doing these calculations for safety related work, I needed a better reason to disregard the test than a hunch and a numerical experiment.  The attached word file is my attempt at proving that the test will never pass for nonzero randomly distributed perturbations when the converged source is uniform.

I am interested in knowing if anybody else has run into this issue and if there is any discussion of this elsewhere.  Specifically if ORNL staff knows about this issue and has documented the failure of the test, it would help me in my own documentation.

[Paul Smith]

The same spreadsheet with a peaked source is attached.

I recognize that my numerical experiment does not properly normalize the distribution, though I don't think that the test relies on a normalization.

[Cliff Dugal]

A few years later and using SCALE 6.3.1, I'm seeing the same thing for a single water-reflected HEU cube. There aren't any convergence issues, yet Shannon entropy test #1 fails. I'd love to hear ORNL's take on this issue too.

An example input file to reproduce this issue:

=csas5
HEU-MET-THERM-003_case01: Oralloy HEU cube on Lucite plate in water
ce_v8.0_endf

read composition
 u-234    1 0 4.9138e-04  300  end
 u-235    1 0 4.5095e-02  300  end
 u-238    1 0 2.3549e-03  300  end

 h-lucite 2 0 5.7744e-02  300  end
 c        2 0 3.6090e-02  300  end
 o        2 0 1.4436e-02  300  end

 h        3 0 6.6740e-02  300  end
 o        3 0 3.3370e-02  300  end
end composition

read parameter
 gen=65
 npg=10000
 nsk=5
 htm=no
 scd=1
end parameter

read geometry
 unit 1
  cuboid 3 1 39.956 -39.956 39.956 -39.956  29.210  5.4315

 unit 2
  cuboid 1 1 5.4315 -5.4315 5.4315 -5.4315  5.4315 -5.4315
  cuboid 3 1 39.956 -39.956 39.956 -39.956  5.4315 -5.4315

 unit 3
  cuboid 2 1 22.789 -22.789 22.789 -22.789 -5.4315 -6.7015
  cuboid 3 1 39.956 -39.956 39.956 -39.956 -5.4315 -6.7015

 unit 4
  cuboid 3 1 39.956 -39.956 39.956 -39.956 -6.7105 -29.210

 global unit 5
  array 1 -39.956 -39.956 -29.210
end geometry

read array
 ara=1 nux=1 nuy=1 nuz=4 fill 1 2 3 4 end fill
end array

read grid 1
 title="5 x 5 x 5 Cartesian mesh which overlays the fissile cube"
 numxcells=5 numycells=5 numzcells=5
 xmax=5.4315 xmin=-5.4315
 ymax=5.4315 ymin=-5.4315
 zmax=5.4315 zmin=-5.4315
end grid

end data
end