Stabilization of multi-group neutron transport with transport-corrected cross-sections

Abstract

Many deterministic neutron transport solvers rely on the source iteration method to solve the multi-group neutron transport equation. Often, these solvers rely on transport corrected cross-sections for accurate prediction of the neutron flux distribution. Transport corrected within-group scattering cross-sections can become negative, and if these negative cross-sections are large in magnitude, source iteration can become unstable and fail to converge for certain cases. In this study, we present evidence of this convergence issue for the method of characteristics (MOC) on full-core PWR problems with common transport correction schemes. A theoretical discussion is presented to illustrate the reason for the convergence issues. Previously established stabilization methods are compared with a newly proposed stabilization method. Results show that the new stabilization method allows for faster convergence than previous techniques. In addition, the effect of Coarse Mesh Finite Difference (CMFD) acceleration on stability is analyzed, showing that CMFD acceleration with full-group structure can overcome the convergence issues, but a stabilization technique is necessary for convergence when a condensed group structure is used.