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Final verification--test against proven code

The final and most valuable test one can apply is to compare the computed solution to a solution produced by an old generally accepted computer code.

At RISØ they have a computer code, DIFF2D, which solves the 1-D or 2-D multi-group diffusion equations. This code was fed with the data for the super-critical test reactor described in section 4.2 and (4.3) and the resulting flux solution is seen in Figure 4.21.

The eigenvalue calculated by the C-function, $\lambda_{0,{\mbox{\protect\scriptsize C}}}$, is

$$\lambda_{0,{\mbox{\protect\scriptsize C}}} = 1.07360$$ (4.24)

which we must compare to the eigenvalue obtained by DIFF2D, $\lambda_{0,{\mbox{\protect\scriptsize DIFF2D}}}$, which has a value of

$$\lambda_{0,{\mbox{\protect\scriptsize DIFF2D}}} = 1.07292$$ (4.25)

When we compare these results we have to bear in mind that the results from (the rather old) DIFF2D code is obtained from calculations in single precision, and that the convergence criterion on the eigenvalue (as stated many times previously it is better to apply a convergence criterion on the eigenvector) was 10^-3, ie rather lax.

When these factors are taken into account we have to conclude that the C-function solution closely resembles the one obtained by DIFF2D.

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