On the benefit of using both hand calculation methods and computer experiments algorithms to solve complex nuclear criticality safety problems - 14299
A companion paper shows the 'anomalies', and even the safety issues, that may be raised by the very usual problem of making safe a fissile mass inside a controlled geometry. These anomalies mainly come from the solving of such problems which belong to the mathematical family of 'robust inversion' including two inversion parameters (the fissile mass and the geometry) and one nuisance parameter (the moderation ratio of the fissile material). Since a 'brute force' method of resolution requires a lot of calculations and since a 'smart' method of resolution requires a lot of engineer time, it is tempting to solve these problems by a 'custom made' approach rather than to achieve a 'whole' resolution. The present paper shows how one can use a hand calculation method (derivation of the one-speed diffusion theory) to perform the whole resolution of such kind of problems with a minimum calculations and human efforts. The powerful capability of predicting the 'anomalies' highlighted in the companion paper is shown. Then the limitations of such a method are discussed: limitation in the geometry of the problem and bias in absolute values prediction. Finally, new algorithms of computer experiments design, dedicated to solve robust inversion problems and based on Kriging surrogates, are tested to solve these problems with limiting calculations and human efforts. The performance of these new algorithms may supplement the one-speed diffusion theory limitations. (authors)