Iterative Homogenization Method for Improving Computational Efficiency in Solving Eigenvalue Problems in Neutron Transport
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The neutron transport equation often is homogenized in order to simplify its solution procedure in some manner or another. There exist many methods for homogenizing the neutron transport equation with different benefits and detriments. One promising method is the Consistent Spatial Homogenization (CSH) method developed and implemented in 1-D by Yasseri and Rahnema. The method, along with its successor, the Diffusion-Transport Homogenization (DTH) method are promising for their ability to reconstruct accurate fine-mesh angular flux profiles as well as reactor eigenvalue after a re-homogenization procedure. This work will explore the extension of both the CSH and DTH methods to higher spatial dimensionality in order to solve large-scale reactor eigenvalue problems. The CSH and DTH methods are based around iterated re-homogenization of the neutron transport equation with an auxiliary source term which is used to correct for heterogeneity effects of a given problem. The net effect of this is that the effects of heterogeneity are relegated to a source term, and the homogenized neutron transport equation is solved instead of the heterogeneous equation. This allows for implementation of simpler acceleration techniques to improve the speed and accuracy of the homogenized problem and in multiple dimensions helps to avoid the effects of complicated reactor geometries. The re-homogenization procedure brings the flux solution back to the heterogeneous discretization in order to generate better approximations for the homogenized cross sections, a better approximation of the auxiliary source term, and most importantly to reconstruct the full heterogeneous angular flux profile. In this work, the CSH and DTH methods are modified for increased spatial dimensionality and implemented using a 2-D SN discrete ordinates transport solver. This implementation is tested using Cartesian-mesh variants of the 2D-C5G7 benchmark problem and a 2-D full-scale boiling water reactor (BWR) benchmark problem.