Stability and Effectiveness of a DSA Scheme Having Two Diffusion Cells Per Transport Cell
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Date
2022-04-20
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Abstract
The purpose of this thesis is to detail the analysis on the stability and effectiveness of a DSA
scheme having two diffusion cells per transport cell. The inspiration to look into such a scheme
originated from Ryosuke Park’s recently published work on an unconditionally stable HOLO
scheme, however, it should be noted that what we analyzed is not equivalent to Ryosuke’s method. The only concept from his method explored in this thesis was the idea of having two diffusion cells per transport cell. To accomplish this, a homogeneous, 1-D slab geometry version of the SN equations with isotropic scattering, and a zero distributed source was discretized with a standard lumped linear-discontinuous Galerkin source iteration scheme and accelerated with a cell-centered diffusion equation for the iterative errors in the scalar fluxes on a sub-mesh for the preconditioning step. A test problem with an incident flux and reflective boundary conditions on a 1000 cm slab was used to experimentally measure the spectral radius. A Fourier analysis was also performed on the error reduction matrix of the full scheme to analytically measure the spectral radius under the same conditions as the experiment. Both of these results were in agreeance and showed that having two diffusion cells per transport cell by itself does not lead to an unconditionally stable system.
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Keywords
HOLO, DSA, Neutron Transport, Fourier Analysis, Diffusion Synthetic Acceleration, High Order Low Order, LDG, Linear discontinuous Galerkin, Finite Element