A physical interpretation and benchmarking of nodal diffusion error estimators

An error estimator application was evaluated for the analysis and interpretation of nodal solutions of the neutron diffusion problem extended to reactor core level. This error estimator application relies on the residual of the equation and gives a global and local characterisation of approximate solutions by the determination of unbalances in the phase-space discretisation. It has been provided a physical meaning in terms of spurious or strange neutron reactions per cubic centimetre and second. The error estimator was applied to a wide scenario of benchmark problems, twelve of which are here reported, with the purpose of comparison between classical quality criteria and the new quality criterion based on the error estimator. The results show that the new observation criterion is able to qualify the approximate solutions in coincidence with the classical criteria but more simply and directly, concluding that approximate solutions producing a global unbalance of about (1(10)), (1(100)), (1(1000)) spurious reactions per neutron removed are respectively unacceptable, reasonably acceptable or very precise. This is achieved systematically and rigorously in the global sense because it is not possible to get an absolute local error for the diffusion problem without the help of a complementary solution; however, the observation of local errors provides valuable, practical insight into the nature of the optimal solution obtainable