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Nonlinear Diffusion Acceleration Method with Multigrid in Energy for k-Eigenvalue Neutron Transport Problems

Luke R. Cornejo, Dmitriy Y. Anistratov

Nuclear Science and Engineering / Volume 184 / Number 4 / December 2016 / Pages 514-526

Technical Paper /

First Online Publication:November 9, 2016
Updated:December 7, 2016

We present a multilevel method for solving multigroup neutron transport k-eigenvalue problems in two-dimensional Cartesian geometry. It is based on the nonlinear diffusion acceleration (NDA) method. The multigroup low-order NDA (LONDA) equations are formulated on a sequence of energy grids. Various multigrid cycles are applied to solve the hierarchy of multigrid LONDA equations. The algorithms developed accelerate transport iterations and are effective in solving the multigroup NDA low-order equations. We present numerical results for model reactor-physics problems with a large number of groups to demonstrate the performance of different iterative schemes.