Eur. Phys. J. Plus (2020) 135: 235
https://doi.org/10.1140/epjp/s13360-020-00216-y

Regular Article

High-accuracy neutron diffusion calculations based on integral transport theory

¹ The Unit of Nuclear Engineering, Ben-Gurion University of the Negev, 8410501, Beersheba, Israel
² CEA, DEN, Service d’études des réacteurs et de mathématiques appliquées (SERMA), Université Paris-Saclay, 91191, Gif-sur-Yvette, France

^* e-mail: gilade@bgu.ac.il

Received: 20 May 2019
Accepted: 8 January 2020
Published online: 10 February 2020

Abstract

In this paper, the Ronen method is developed, implemented, and applied to resolve the neutron flux and the criticality eigenvalue in simple one-dimensional homogeneous and heterogeneous problems. The Ronen method is based on iterative calculations of correction factors to use in a multigroup diffusion model, where the factors are actually given by the integral transport equation. In particular, spatially dependent diffusion constants are modified locally in order to reproduce new estimates of the surface currents obtained by the integral transport operator. The diffusion solver employed in this study uses finite differences, and the transport-corrected currents are introduced into the numerical scheme as drift terms. The corrected solutions are compared against reference results from a discrete ordinate code. The results match well with the reference solutions, especially in the limit of fine meshes, but slow convergence of the scalar flux is reported.