Convergence Analysis for the CMFD Accelerated Linear Axial Expansion Transport Method Based on Fourier Analysis

The linear axial expansion transport method avoids the negative source problem caused by transverse leakage in the traditional two-dimensional/one-dimensional (2D/1D) transport method and has better stability. However, stability is poor with the coarse-mesh finite difference (CMFD) accelerated linear axial expansion transport method. In this paper, the stability of the partial current–based coarse-mesh finite difference (p-CMFD) method, the optimally diffusive coarse-mesh finite difference (od-CMFD) method, and the linear prolongation coarse-mesh finite difference (lp-CMFD) method is studied based on Fourier analysis. The results of the Fourier analysis indicate that the problem is stable for axial coarse-mesh optical thickness less than 2 or larger than 50; the calculation diverges when the axial coarse-mesh optical thickness is between 2 and 50. The numerical results of the KUCA benchmark problem are the same as the results of the Fourier analysis.