High Fidelity Deterministic Solution of Neutron Transport Problems in Graphite

The study of thermal radiative transfer in the high energy density regime is important to the National Nuclear Security Administration, and experiments are an important component of such studies. Strong non-linear coupling of radiation hydrodynamics and thermal radiation transport makes it difficult to infer radiation transport uncertainties from experiments. In order to address this problem and have a hierarchical approach to model validation, the Center for Exascale Radiation Transport (CERT), created at Texas A&M University, has designed neutrons-in-graphite experiments as surrogates for thermal radiative transfer in high energy density. There is a strong mathematical analogy between the process of radiative absorption and emission, and the process of neutrons scattering in highly diffusive mediums. This allows the solution for thermal radiation transport benchmark problems to be measured by the neutrons-in-graphite surrogate experiments. The CERT team has designed a series of neutrons-in-graphite experiments to allow investigation of many of the significant transport difficulties regarding thermal radiative transport including: multi-scale modelling in time, space, and angle; highly scalable parallel solution techniques; and refinement in time, space, and angle. The development of computation methods to efficiently and accurately simulate the neutrons-in-graphite surrogate experiments and the predictive science methods to quantify the uncertainty will also be applicable to the analogous thermal radiation transport simulations. This thesis systematically investigates the required spatial, angular, and energy resolution needed to obtain high-fidelity deterministic transport solutions for the neutrons-in-graphite experiments designed as surrogates for thermal radiative transfer. Semi-analytic and stochastic methodologies are considered in order to investigate the deterministic neutron transport discretization error as a function of the spatial, angular, and energy resolution. For the discretization error calculations, a hierarchical approach is taken towards increasingly complex geometries. Infinite graphite medium problems with a uniform source have only energy dependence. The infinite medium problems are used to compute the deterministic multi-group discretization error as a function of the energy resolution. 2D graphite problems with an infinite line source and 3D graphite cube problems with a point source are modelled to analyze spatial and angular discretization error as a function of spatial and angular resolution. An analysis is performed on the angular discretization ray effect errors that are present in deterministic discrete ordinate calculations. This research informs the uncertainty quantification efforts for CERT and points the way to the further development of deterministic calculations