Dynamic implementation of the equivalence theory in the heterogeneous whole core transport calculation

Abstract

The coarse mesh finite difference (CMFD) formulation is applied to the heterogeneous whole transport calculation as a means of efficient acceleration as well as simplified representation. A pin cell is chosen as the base coarse mesh which is much coarser than the intra-cell flat source regions. The CMFD formulation enables dynamic homogenization of the cells during the iterative solution process such that the heterogeneous transport solution can be preserved. Dynamic group condensation is also possible with a two-level CMFD formulation involving alternate multigroup and two group calculations. The two-dimensional method of characteristics (MOC) is used as the kernel to generate the heterogeneous solution and the CMFD solution provides the MOC kernel with much faster converged fission and scattering source distributions. Through the applications to various problems including different compositions, sizes, and energy groups, it is shown that the performance of the CMFD formulation is superior in that the number of the MOC calculations can be reduced below 10 while reproducing exactly the original transport solution. The merit of the CMFD formulation is greater for larger problems in which speedups of 100-300 are possible when compared to the unaccelerated case.