On the multigroup albedo boundary conditions for discrete ordinates nuclear reactor global calculations in X,Y-rectangular geometry

Presented here is a study on the use of approximate albedo boundary conditions, for numerically solving multigroup discrete ordinates (S_N) neutron transport eigenvalue problems, in two-dimensional Cartesian geometry for nuclear reactor global calculations in homogenized assembly chessboard models. A matrix operator, referred to as multigroup albedo matrix, approximates the non-multiplying regions that typically surround the cores of nuclear reactors (e.g., baffle and reflector), by neglecting the transverse leakage terms that arise from transverse integrations of the X, Y-geometry multigroup S_N neutron transport equations within these regions. These approximate albedo matrices are obtained through convenient manipulations of the coarse-mesh Spectral Greeńs Function (SGF) method’s auxiliary equations and are applied to the traditional fine-mesh Diamond Difference (DD) method in reactor global calculations, aiming at shortening the computer running time by substituting the non-multiplying regions around the core through the offered albedo boundary conditions. Numerical results are provided for one typical two-group model problem to illustrate the accuracy of the numerical results and computer running time of the computer code implementing the proposed approach.