Calculation of the eigenfunctions and corresponding eigenvalues of the two-group diffusion equation in heterogeneous systems

This paper deals with the extension of an existing code developed at the Department of Nuclear Engineering, Chalmers University of Technology, to the calculation of the higher order eigenfunctions and corresponding eigenvalues of the two-group diffusion equations. More specifically, this code, originally meant for calculating the two-group static neutron flux and its adjoint for any two-dimensional heterogeneous system, is modified in order to calculate any higher mode of both the neutron flux and its adjoint. A one-dimensional two-region system is first considered for benchmark purposes, where the reference solution can be determined semi-analytically. The numerical solution is computed using a modified power iteration method. The agreement between the numerical solution and the reference solution is found to be excellent, both regarding the eigenfunctions and the eigenvalues, and both for the forward and adjoint problems. The modified power iteration method is then applied to the calculation of the different modes of the neutron flux and its adjoint in a two-dimensional heterogeneous representation of the Swedish Forsmark-1 BWR core corresponding to the 1996/1997 channel instability event