Introducing the migration mode method for the solution of the space and energy dependent diffusion equation

The most usual method to take into account energy dependence in whole core spatial neutronics calculation is the multigroup method. In thermal spectrum reactors as PWR, two-group theory is sufficient to describe accurately the neutron spectrum variation among spatial regions. When the spectrum hardens the precision of two-group theory decreases and more groups are necessary to keep a good accuracy. The aim of the computation method presented here is to represent with a good accuracy the spectral transitions which appear in these situations, without increasing the number of unknowns (i.e. the number of energy groups). The neutron spectrum is considered as a combination of base shapes corresponding to the different modes of migration of the neutrons in the energy dimension. The resulting energy flux distribution is a continuous function that fits the real one. The spatial discretization leads to matrices having the same structure of the ones obtained with multi-group theory. Then the method can be easily applied to existing codes solving the diffusion equation on the whole core in 3D. A methodological comparison between the migration mode method and the multigroup (few-group) method as well as a numerical comparison is presented.