4 - Neutron transport calculations at the core level

Abstract

In this chapter, the methods used for solving the neutron transport equation at the core level are presented. It is assumed that prior to using these methods, a proper set of multi-group cross-sections, diffusion coefficients and possibly assembly discontinuity factors have been estimated and prepared, with a spatial and energy resolution compatible with the one to be used by the core simulators. In the first part of this chapter, the angular discretization of the neutron transport equation is described with three methods explained: the spherical harmonics (PN) method, the diffusion theory method and the simplified PN method. In the second part of the chapter, the spatial discretization is touched upon. Since most core simulators use diffusion theory or equivalent methods, emphasis is put on diffusion theory, with again three methods presented: finite difference methods, nodal methods and finite element methods. Thereafter, the solution procedure for estimating the core-wise position-dependent multi-group neutron flux is described. Finally, the methodology used for determining the core-wise space- and time-dependent neutron flux in case of non-steady-state situations is derived.