Coarse Mesh Finite Difference Acceleration of Discrete Ordinate Neutron Transport Calculation Employing Discontinuous Finite Element Method

Abstract

The coarse mesh finite difference (CMFD) method is applied to the discontinuous finite element method (DFEM) based discrete ordinate (SN) calculation for source convergence acceleration. The 3-D DFEM-SN code FEDONA is developed for general geometry applications as the framework for the CMFD implementation. The characteristic features and validation results of FEODNA are presented first including the capability of a parallel computing. The detailed methods for applying the CMFD acceleration are then established, such as the method to acquire the coarse mesh flux and current by combining unstructured tetrahedron elements in rectangular coarse meshes and the alternating calculation method to exchange the updated flux and current information between the CMFD and DFEM-SN. The partial current based CMFD (p-CMFD) is also implemented for assessment of the acceleration performance. The modified p-CMFD method is proposed to correct the weakness of the original p-CMFD formulation. The performance of CMFD acceleration is examined first for a group of simple two-dimensional multigroup problems that are designed to investigate the effect of the problem and coarse mesh sizes. It is shown that the CMFD acceleration becomes more efficient as the problem size increases and also that using smaller coarse meshes are more advantageous. The p-CMFD, however, shows inferior performance than the CMFD while the modified p-CMFD shows similar effectiveness as the standard CMFD. For the analytic comparison of the convergence performance for the CMFD variations, the Fourier analysis is performed for three methods. The effectiveness of CMFD acceleration is then assessed for three-dimensional benchmark problems such as the IAEA and C5G7MOX problems. It is demonstrated that a sufficiently converged solution is obtained within about 7 outer iterations which would require 175 iterations with the normal DFEM-SN calculations for the IAEA problem. It is claimed that the CMFD accelerated DFEM-SN method can be effectively used in the practical eigenvalue calculations involving general geometries.