Techniques for Stabilizing Coarse-Mesh Finite Difference (CMFD) in Methods of Characteristics (MOC)

Abstract

The Coarse-Mesh Finite Difference (CMFD) method has been widely used to effectively accelerate neutron transport calculations. It was however found to be at times unstable in the presence of strong heterogeneities. The common practice to improve stability is to employ a damping factor on the nonlinear diffusion coefficient terms, but there is no method to determine the optimal damping factor for a practical reactor problem prior to the calculation. This paper investigates two problem-agnostic techniques that stabilize reactor calculations that would otherwise diverge with undamped CMFD. The first technique is to perform additional energy sweeps for the upscattering group region during the high-order MOC calculation to generate more accurate information to pass into the CMFD calculation. The second technique extends the traditional scalar flux prolongation to provide spatial variations inside each acceleration cell. This study uses the 2D C5G7 problem and the Babcock & Wilcox 1810 series critical experiment benchmark to evaluate these methods. Numerical simulations showed that both techniques stabilize CMFD, and that the linear prolongation technique did not incur additional computational cost compared to the optimally damped conventional method