Numerical algorithms for intragranular fission gas release

Complicated physical processes govern fission gas release in nuclear fuels. Besides the physical problem, there is a numerical problem since some solutions of the underlying diffusion equation have numerical errors that by far exceed the physical details. In this paper, the efficiency and the accuracy of some numerical solutions are analysed. Random operation histories were generated and the errors inherent in each algorithm evaluated over a wide range of up- and down-ramps by comparing the results with the quasi-exact ANS-5.4 algorithm. The URGAS algorithm can be considered as well balanced over the entire range of fission gas release. The new FORMAS algorithm is superior at fission gas release above f∼0.05 and may in a physical sense be considered as an exact solution in this range. Unfortunately, the deficiency of this most elegant and mathematically sound algorithm at low fission gas release could not be fully overcome. However, in view of the many inherent uncertainties, both algorithms are considered as sufficient to be used in a fuel rod performance code. All algorithms analysed in detail can be made available on request as FORTRAN subroutines