Convergence study of traditional 2D/1D coupling method for k-eigenvalue neutron transport problems with Fourier analysis

Abstract

2D/1D coupling method is an important neutron transport calculation method due to its high accuracy and relatively low computation cost. However, 2D/1D coupling method may diverge especially in small axial mesh size. To analyze the convergence behavior of 2D/1D coupling method, a Fourier analysis for k-eigenvalue neutron transport problems is implemented. The analysis results present the divergence problem of 2D/1D coupling method in small axial mesh size. Several common attempts are made to solve the divergence problem, which are to increase the number of inner iterations of the 2D or 1D calculation, and two times 1D calculations per outer iteration. However, these attempts only could improve the convergence rate but cannot deal with the divergence problem of 2D/1D coupling method thoroughly. Moreover, the choice of axial solvers, such as DGFEM SN and traditional SN, and its effect on the convergence behavior are also discussed. The results show that the choice of axial solver is a key point for the convergence of 2D/1D method. The DGFEM SN based 2D/1D method could converge within a wide range of optical thickness region, which is superior to that of traditional SN method.