Fourier analysis of two-dimensional discrete ordinates method for solving multigroup neutron transport k-eigenvalue problems

Convergence study of two-dimensional discrete ordinates (SN) method has been carried out by Fourier analysis for single-group neutron transport k-eigenvalue problems. However, conclusions and improved coarse mesh finite difference (CMFD) acceleration method derived from single-group Fourier analysis are not fully applicable to the realistic multigroup problems. The convergence characteristic of two-dimensional SN for multigroup problems has not been systematically investigated, which is an important work that complements the existing studies. In this study, a Fourier analysis for solving multigroup neutron transport k-eigenvalue problems is performed. Firstly, the influence of multigroup structure is analyzed and results show that when neglecting the intergroup scattering, the spectral radius of multigroup case is the maximum value of all the single-group cases. Then, the effects of scattering ratio on the convergence behavior are presented. Fourier analysis results show that when increasing the within-group scattering ratio, the spectral radius of the whole iteration decreases. While for the intergroup scattering ratio, the phenomenon is totally opposite. When increasing the intergroup scattering ratio, the spectral radius increases. Lastly, the diffusive coefficient of CMFD is guided based on the Fourier analysis results, which considering the influences of the intergroup scattering. Numerical results show that improved CMFD achieves better convergence performance for 2D C5G7 benchmark and especially for high intergroup scattering problems.