Finite Difference Equations for Neutron Flux and Importance Distribution in 3D Heterogeneous Reactor with Unstructured Mesh

Abstract

In the paper, algorithms of the surface harmonics method (SHM) for deriving finite difference (algebraic) equations to describe the neutron field in a heterogeneous reactor are developed. The neutron transport equation is used as the initial equation. The step of deriving the diffusion equation in the differential form is omitted. The paper contains no assumptions on the symmetry of the reactor unit cells (unstructured mesh is accepted) or on the possibility to describe the neutron distribution at the cell boundaries in the diffusion approximation for deriving the equations. It is computationally shown that rejection of the diffusion approximation at the cell boundaries considerably improves the accuracy of solutions of the test problems.