A Neutron Transport Characteristics Method for 3D Axially Extruded Geometries Coupled with a Fine Group Self-Shielding Environment

Abstract

In this paper we describe some recent developments in the Method of Characteristics (MOC) for three-dimensional (3D) extruded geometries in the nuclear reactor analysis code APOLLO3^®. We discuss the parallel strategies implemented for the transport sweep of the MOC solver in the OpenMP framework, and introduce the 3D version of the DP_N operator that is customarily used in APOLLO2 to accelerate MOC convergence. In order to provide good physical results, we have also coupled the MOC with the self-shielding environment of APOLLO3^®. We describe, in particular, the coupling techniques necessary to implement a full subgroup cross-section self-shielding method and a specialized version of the Tone self-shielding technique. In this framework, we use part of the tracking method used for the 3D calculation to provide the two-dimensional Collision Probability Method (CPM) coefficients necessary to produce the self-shielding calculations. We will show some important computational speedups also in the CPM of APOLLO3^® with respect to the APOLLO2 CPM equivalent implementation, including the parallelization issue. Finally, we will compare our approach toward a Monte Carlo calculation of a fast breeder reactor hexagonal assembly representing a fertile-fissile interface.

Keywords:

• 3D method of characteristics
• self-shielding methods
• synthetic acceleration techniques

Acknowledgments

The authors would like to acknowledge AREVA and EDF for their long-term partnership and support in the development of the APOLLO3^® nuclear reactor analysis code. We thank J. F. Vidal, J. M. Palau, and P. Archier for having provided the 3D FBR assembly case that has been used to benchmark our developments. We also want to thank the reviewers for their valuable comments that have strongly improved the quality of this paper.

Notes

^a We recall that with the term “compound” trajectories,^34,50 we refer to the set of subtrajectories that can be built tracking an arbitrary geometrical domain surrounded by boundary conditions that can be represented by a geometrical movement of trajectory such as rotation, translation, or symmetry. The global trajectory is then constituted by the set of “compound” ones, in which the starting point of each new compound trajectory is obtained by applying the “geometrical movement” related to the boundary condition.

^b When leakage model calculations are run and the buckling term is affected via the total cross sections, one can eventually have τ_min < 0. For this reason we cannot simply assume τ_min = 0.

^c The only drawback of this approach relies on the length of the table that can arbitrarily grow, worsening memory swap. In our experience it is better to elude conditional testing and leave the computer managing a bigger table. A qualitative explanation for this is that even if the memory accesses to the table are random, the greater part of accesses are for relatively small values of τ. Table values for large optical lengths are to be considered “pathological” and related to computational regions where chords with optical lengths of some decades are possible. Such situations are related to poorly spatial-converged regions whose existence is hopefully rare when the geometrical model is physically correct. Therefore, if one supposes that these events are sporadic, the cost of repaginating memory to search the part of the table containing higher values should be reduced.