Solving the multigroup integro-differential equation of the neutron diffusion kinetics in 3D-Cartesian geometry

The multigroup time-integro-differential equation of the neutron diffusion kinetics (IDE-NDK) was solved numerically in 3D Cartesian geometry with the use of the basic-progressive polynomial approximation (BPn) using the finite difference method (FDM) for the spatial discretization. Applications involving ramp and instantaneous change of the thermal removal or fission macroscopic cross sections were used to assess the accuracy of the BP2 algorithm. Two reactor models were used: a homogeneous and the 3D-TWIGL reactor. The BP2 algorithm showed good accuracy when it is compared to the results of other codes. Also the static neutron diffusion equation was solved numerically with the Lagrange interpolation polynomial to assess the Keff accuracy of the FDM used for the steady state problem. In some applications calculations were performed as function of the time integration step and mesh size. Extrapolations to infinitesimal mesh size were performed in some cases.