One-node CMFD formulations for multi-group SP3equations in hexagonal geometry

Abstract

In this study, one-node CMFD formulations are proposed for multi-group SP3equations in hexagonal geometry. The key idea of these formulations is to define the SP3partial currents, which are derived from Marshak-like boundary conditions of the SP3 analysis. The SP3partial currents can be interpreted as information-transfer-kernels for the non-linear iteration. The one-node CMFD formulations for SP3method also encounter unstable convergence issues similar to the conventional two-node CMFD acceleration method. To overcome these convergence problems, the FF-CMFD method is applied for one-node CMFD formulations by introducing the biased second order moment. The one-node CMFD formulations for SP3analysis are verified by solving the reference reactor core, PGSFR, which consists of 9-group homogenized materials. In order to emphasize the impact of control rods insertion, the problem is solved with and without the control rods. The SP3analysis can be compared to the diffusion analysis in terms of accuracy depending on the control rod assemblies. In addition, the efficiency of parallel calculation is verified by using OpenMP depending on the number of CPU cores. The parallel efficiency of one-node CMFD for the SP3method can be as high as the one-node CMFD diffusion method.