A two grid acceleration scheme for the nodal diffusion equation in hexagonal geometry

Abstract--A two grid acceleration scheme for the solution of the nodal diffusion equation in hexagonal geometry has been formulated. The proposed scheme also involves the linear shifting of the keff values during each iteration in both the coarse nodes as well as the fine nodes for accelerating the initial stages of the solution. The partially converged solutions of the nodal diffusion equation in the coarse nodes and fine nodes are used to predict a parameter for acceleration of the flux and fission source convergence in the subsequent iterations in the fine node grid. The effectiveness of the iteration scheme was tested by incorporating it in the NOD HEX program which solves the multigroup diffusion equation in 2-D by the Nodal Expansion Method. The VVER-lOOO, SNR-300 reactor core benchmarks and a proposed 500 MWe LMFBR were analysed. The results were compared with the results of the calculation using the Chebyshev two parameter acceleration scheme for flux convergence and without any acceleration scheme in the NODHEX program. The two grid acceleration scheme is found to be in most cases more efficient than the commonly used Chebyshev acceleration scheme