Development of SUBSPACE-Based Hybrid Monte Carlo-Deterministic Algorithms for Reactor Physics Calculations

This dissertation develops an innovative hybrid Monte-Carlo-Deterministic (MC-DT) method which places high premium on attaining high computational efficiency for reactor analysis applications. Over the past few decades, there have been a plethora of techniques proposed to enable the hybridization of MC and DT methods with great success primarily for shielding applications where one is often interested in estimating the flux at few given points. The basic idea is to employ a simplified deterministic model to get an estimate of the flux solution, which is subsequently employed to bias the MC particles. In one implementation, adjoint deterministic calculations are employed to set weight-windows to accelerate convergence of MC simulation. Some progress has been made recently for reactor analysis applications where one is interested in calculating the flux distribution everywhere in the reactor core, which is much more computationally demanding than shielding applications because of the huge increase in the number of responses required. We believe the efficiency of these methods however is still too low to enable using MC methods in routine analysis calculations where typically one needs to execute the flux solver in the order of 103-105 times. To be acceptable to nuclear practitioners, e.g. fuel vendors and utilities, the efficiency of hybrid MC-DT needs to method that of existing deterministic methods used for routine design calculations. This dissertation contributes a new hybrid method denoted hereinafter by the SUBSPACE method, which primarily focuses on improving the efficiency of hybrid methods for reactor analysis applications, whereby highly accurate estimates of the energy-dependent flux are required everywhere in the reactor core, including a detailed pin power distribution for each fuel assembly. The SUBSPACE method achieves its higher computational efficiency by taking advantage of the correlations between the responses. These correlations are introduced by the physics of radiation transport. Research over the past ten years has shown that the effective degrees of freedom in reactor analysis problems are very few despite the high dimensionality of the associated models. The SUBSPACE method takes advantage of this situation by identifying a small number of degrees of freedom towards which the MC particles are biased in a similar manner to existing hybrid methods. Significant gains in computational efficiency have been demonstrated using this method. The dissertation derives the mathematical theory behind the SUBSPACE method and applies it to realistic reactor analysis models. Two different implementations of the SUBSPACE method are presented, the first one described above relies on an adjoint deterministic model to calculate weight-windows for MC particles biasing. The second one is referred to the Gaussian Process (GP) method. The reason for this name is that the responses correlations are captured based on the assumption that the responses can be treated as Gaussian processes, which is a reasonable assumption for radiation transport. The applicability of the SUBSPACE method is also demonstrated for different types of models, including k-eigenvalue core-wide models, assembly models used for cross-sections homogenization for subsequent core-wide calculations, and depletion calculations. Given the favorable results obtained here, we believe the applicability of the MC method for large scale reactor analysis could be realized over the near future.