A stable algorithm for calculating one-group diffusion coefficient in a multi-zone cylindrical cell by the surface pseudo-sources method

Abstract

In the surface harmonics method, designed to solve the neutron transport equation of in the core of a nuclear reactor, the distribution function is decomposed by trial functions. The first trial function is the absorption and division matrix. It is responsible for the main processes (absorption and fission) that occur inside the nuclear reactor cell. The second trial function is the diffusion coefficient matrix. It is associated with the processes of neutron flow from one cell to another. It is usually calculated in the P2 – and P4 – approximations of the spherical harmonics method and by the surface pseudo-sources method. In close lattices with high absorption of P2 – and P4 – approximations may not be enough, and the surface pseudo-sources method proves to be unstable in the calculation of multi-zone cylindrical cells. This work is dedicated to the development of stable one-group calculation of the diffusion coefficient by the surface pseudo-sources method first, by eliminating the divergent integrals, and secondly, the modification of the algorithm of matrix factorization for calculating one-group neutron transport equation. Developed program DICOF may use in the complexes of WIMS-SH and SVL for stable calculation of the diffusion coefficients matrix for calculation of the VVER and RBMK reactors.