Computational Analysis of a Nuclear Reactor Cell in the Linear-Anisotropic Approximation by the Generalized Method of First Collisions Probabilities

Abstract

This work is devoted to the development of a method for solving the Boltzmann kinetic equation for neutron transport. The method is focused on solving an integral equation for neutron transport in a reactor cell with a complex geometry and different boundary conditions. An algorithm is proposed for solving the problem taking account of anisotropic scattering in the linear-anisotropic approximation. The approach is based on expanding the neutron flux in a system of orthogonal two-dimensional polynomials in each uniform zone of a heterogeneous cell. This expansion reduces the system of linear integral equations to a system of linear algebraic equations. The relations required to calculate the coefficients in the equations (six-fold integrals) as well as the computational algorithm are presented. Calculations of cylindrical and cluster cells are presented. The calculations are compared with the surface pseudosource method. It is shown that the results have advantages over the method of first collisions probabilities.