Parallel 3-D Method of Characteristics with Linear Source and Advanced Transverse Integration

Abstract

In the design and analysis of nuclear fission reactor systems, simulations are an essential tool for improving efficiency and safety. Neutronics simulations have always been limited by the available computational resources. This is because of the large discretizations necessary for the neutron transport equation, which has a 6-dimensional phase space for steady-state eigenvalue problems. The “gold standard” for 3-D neutron transport simulations is Monte Carlo with explicit geometry representation because it treats all dependent variables continuously. However, there are significant remaining challenges for Monte Carlo methods that prohibit widespread use and put them at a disadvantage compared to deterministic methods. The “gold standard” for deterministic 3-D neutron transport is the MoC. Numerous deterministic methods exist for solving the transport equation. Each of them has their own drawback. MoC is considered the “best” due to its ability to accurately model the exact geometry and approximate anisotropic scattering (other methods do just one of these well or become undesirably complex). The downside of the 3-D MoC method is the substantial computational resources required to discretize the problem. There has been renewed interest in assessing the state of the art for MoC and the tractability of this problem on the newest computer architectures. Previous work made significant strides in parallelizing the 3-D MoC algorithm for 100,000’s of processors, but ultimately did not prove viable due to the extreme compute resources required. Since then there has been progress in making 3-D MoC less computationally burdensome by adopting more advanced discretization methods that lead to fewer spatial mesh regions and rays; namely the linear-source approximation (LSA), and chord-classification or on-the-fly ray-tracing. The goal of this thesis is to continue progress in reducing the computational burden of MoC calculations, with a focus on three-dimensional calculation. This thesis tries to reach this goal through three related contributions: the utilization of graph-theory for spatial decomposition, improvements to the LSA for Multiphysics calculations, and a novel 3-D ray-tracing method with advanced transverse integration. Spatial decomposition is typically very beneficial, if not necessary, for whole-core direct transport methods. Previous works on 3-D MoC calculations have used simple spatial decomposition schemes, that often resulted in poor load-balancing, particularly when using the LSA. This work addresses this issue by utilizing graph partitioning methods to give better load-balance, even in cases where the number of computational cells is very different in different regions of the reactor. The LSA has previously been shown to allow for the use of a coarser mesh while maintaining accuracy in pure neutronics calculations. However, typically the problems of interest involve multiple physics such as isotopic depletion and thermal-hydraulic (T/H) feedback. This work improves the LSA method for such problems by re-formulating the equations to eliminate an inefficiency in cases with non-constant cross sections. This is shown to significantly improve run-times and reduce memory usage, even in such cases. Finally, a novel 3-D ray-tracing method, based on the macroband, is developed to reduce the number of characteristic tracks necessary for accurate results. The method is compared against a traditional ray-tracing method for several benchmark problems. In several of these cases, the method is shown to significantly reduce the number of segments necessary for similar accuracy. The ray-tracing method is also shown to have very desirable properties such as near-monotonic convergence, and can act as more of a “black-box” solver.