A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

Coarse-mesh finite difference (CMFD) method is a widely used numerical acceleration method. However, the stability of CMFD method is not good for the problems with optically thick regions. In this paper, a stability rule named the “sign preservation rule” in the field of numerical heat transfer is extended to the scheme of CMFD. It is required that the disturbance of neutron current is positively correlated with that of the negative value of flux gradient. A necessary condition for stability of the CMFD method is derived, an adaptive diffusion coefficient equation is proposed to improve the stability of CMFD method, and the corresponding revised CMFD method is called the rCMFD method. With a few modifications of the code, the rCMFD method was implemented in the hexagonal-Z nodal S_N (discrete-ordinates) solver in the NECP-SARAX code system. The rCMFD method and other similar acceleration methods were tested by three fast reactor problems which were obtained by modifying the hexagonal pitches of a benchmark problem. The numerical results indicated that the rCMFD method showed better stability than the traditional CMFD method and the artificially diffusive CMFD (adCMFD) method and a better convergence rate than the adCMFD method and the optimally diffusive CMFD (odCMFD) method for these fast reactor problems.