Computational Methods for Multidimensional Neutron Diffusion Problems

A neutronic module for the solution of two-dimensional steady-state multigroup diffusion problems in nuclear reactor cores is developed. The module can produce both direct fluxes as well as adjoints, that is, neutron importances. Different numerical schemes are employed. A standard finite-difference approach is firstly implemented, mainly to serve as a reference for less computationally challenging schemes, such as nodal methods and boundary element methods, which are considered in the second part of the work. The validation of the methods proposed is carried out by comparisons of results for reference structures. In particular a critical problem for a homogeneous reactor for which an analytical solution exists is considered as a benchmark. The computational module is then applied to a fast spectrum system, having physical characteristics similar to the proposed lead-cooled ELSY project. The results show the effectiveness of the numerical techniques presented. The flexibility and the possibility to obtain neutron importances allow the use of the module for parametric studies, design assessments, and integral parameter evaluations as well as for future sensitivity and perturbation analyses and as a shape solver for time-dependent procedures.