Resonance treatment using the Discrete Generalized Multigroup method

Abstract

In reactor physics calculations for reactor design and operations, today's methods rely on approximate models to account for resonance self-shielding effects. A multi-level approach, which includes several levels of calculations where complexity in energy is decreased as spatial complexity is increased, is employed to model nuclear reactors. However, this approach breaks down when alternate materials and reactor designs are considered. Thus, in order to simulate behavior in an unconventional system, higher fidelity methods are desired. Continuous energy or ultrafine multigroup nuclear data allows this high fidelity to be achieved but is associated with a high computational expense. This thesis proposes that the Discrete Generalized Multigroup (DGM) method is a possible means of approximating the high fidelity results associated with an ultrafine energy mesh without the high degree of computational expense. DGM maps the ultrafine group energy mesh to a coarser energy mesh, where transport calculations are performed, through a discrete expansion. Additional data-moments of the expansion-are retained to unfold an approximate ultrafine energy spectrum. A recondensation procedure is used, where the method is applied in succession, allowing details from the coarse group calculation to influence the collapse of the coarse group data. In applying DGM to an ultrafine energy mesh, prohibitive computational expense is seen to exist in the computation of moments of the scattering matrix and in the flux updates used to maintain stability. Means of reducing the computational expense associated with the scattering matrix are suggested, but left to future work. Flux updates are removed by introducing Krasnoselskij iteration and a group mapping algorithm to the DGM recondensation procedure. Krasnoselskij iteration allows recondensation to become convergent by using a portion of the previous iterate when updating the solution vector. The group mapping algorithm places coarse group boundaries where large disparities in fine group cross sections are present, enhancing the stability characteristics of recondensation. These algorithmic changes do not negatively impact the accuracy of the procedure and remove a large computational expense from the method. Ultimately, the method is deemed to be an attractive option for approximating a high fidelity solution.