Validation of the SHNC time-dependent transport code based on the spherical harmonics method for complex nuclear fuel assemblies

Abstract

The diffusion approximation to the time-dependent Boltzmann transport equation gives accurate results for traditional nuclear reactor designs, but new reactor designs and new fuel elements require neutron transport methods. We develop a numerical approximation to the time-dependent transport equation coupled to delayed neutron precursors based on the spherical harmonics PL equations, for odd L, and on the Backward Euler finite difference discretization of time. The resulting scheme can be written as a stationary form of diffusive second order PL equations. This allows a reduction by half to the number of unknowns and also to apply a nodal collocation method to the spatial discretization of the problem, using coarse spatial grids to further reduce memory requirements. This scheme is validated with several transient benchmarks, where the convergence properties are established and compared with the simplified PL approximation. A more realistic transient benchmark, based on the two-group C5 MOX problem, is finally introduced, showing the need of high order PL approximation for complex fuel geometries.