An analysis of condensation errors in multi-group cross section generation for fine-mesh neutron transport calculations

Abstract

When collapsing multi-group cross sections, a flux separability approximation is often used. This assumes the angular variation of the flux is independent of the energy dependence, which avoids angular dependence of the total multi-group cross section. This paper investigates the impact of this approximation on fine-mesh deterministic multi-group transport methods for two PWR pin-cell benchmarks, which demonstrate errors of more than 1% in energy groups with large U-238 capture resonances and an eigenvalue bias of approximately 200 pcm between continuous energy Monte Carlo and deterministic transport methods, even when the “true” scalar flux is used to collapse cross sections. This paper also investigates two means of resolving this issue, but both are seen to have significant short-comings. First, the most direct and mathematically consistent approach is to use angularly-dependent multi-group cross sections. These cannot be easily computed for arbitrary geometries using traditional multi-group cross section generation methods, are not supported by most standard transport codes, and require significant spatial discretization. Second, SuPerHomogéneísation (SPH) factors are used to preserve reaction rates between continuous energy Monte Carlo and deterministic transport methods, but the SPH scheme requires knowledge of the reference source distribution, is dependent on the spatial discretization mesh, and is indiscriminate between various sources of approximation error.