Demonstration
A lattice, solved live.
Surrogate flux
A fast model's answer, two per cent out, with k fitted beside the flux rather than taken from it. The residual is the part that does not look like the solution.
Solved flux
One group diffusion under power iteration, with k taken from the balance of the field it solved for, which is what k means. The residual then closes.
Conservation is structural in the solved lattice, so the neutron balance closes at floating point.
How to read this figure
Every cell of the cube, its brightness the flux it holds.
Five control rods, driven into the lattice and drawn back out. Both columns see the same rods at the same depth.
Cells where the balance does not close, stained. On the left there are many, on the right none.
The vessel, with vacuum at every face.
Conservation is structural in the solved lattice, so the neutron balance closes at floating point. What is measured is the residual of production against absorption plus leakage, taken cell by cell as the rods carry k from 1.038 through critical to 0.952. The solved lattice closes it to fifteen decimal places at every rod depth in the run; the surrogate stops at two per cent, the size of its own flux error, and stays there however long it iterates. The discretisation agrees with the analytic buckling for a bare cube, νΣf = 29.72.