Numerical methods for solving the transport equation in multi-group approximation in three-dimensional geometry in program package “REACTOR”

The numerical methods used in program package “REACTOR” for solving the transport equation in multi-group approximation in rectangular X-Y-Z geometry, hexagonal HEX-Z geometry and cylindrical R-$\varphi$-Z geometry are described in this work. It is the most working time component of program package, intended for calculation of neutron-physical characteristics of reactor core (eigenvalue $K_{\mathrm{eff}}$) and radiation fields by the $S_n$-method of Discrete Ordinates with $P_m$-approximation of scattering cross sections. The distinction from the previous version of program package consists in using the most effective weighted schemes for solving the transport equation and inner and outer iteration acceleration methods. To calculate the eigenvalue the numerical solution obtained in diffusion approximation is used for initial approximation of fluxes. For the shielding problems the distributed fission source in reactor core is used. For example the three-dimensional results of calculation the eigenvalue $K_{\mathrm{eff}}$ and radiation fields are given for SVBR-75/100 reactor plant.