Stability and accuracy of 3D neutron transport simulations using the 2D/1D method in MPACT

Space–time kinetics modeling of Advanced Heavy Water Reactor for control studies

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.

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

Coarse mesh finite difference formulation for accelerated Monte Carlo eigenvalue calculation

As an effort to establish a fast, yet accurate multigroup nodal solution method that is crucial in repeated static and transient calculations for advanced reactors, the source expansion form of the semi-analytic nodal method (SANM) is introduced within the framework of the coarse mesh finite difference (CMFD) formulation. The source expansion is to expand the analytic form of the source appearing in the groupwise neutron diffusion equation with a set of orthogonal polynomials in order to obtain a group decoupled analytic solution. Both one- and two-node formulations are examined to determine the best nodal kernel. For the acceleration, a two-level CMFD scheme is established employing a multigroup and two-group CMFD. In addition, an alternative two-node direct SANM formulation with a quartic polynomial is examined to assess the direct vs. iterative resolution of the group coupling. The performance of the CMFD formulation with three different multigroup SANM nodal kernels is examined for a wide variety of multigroup benchmark problems including several MOX-loaded LWR cores and large FBR cores. It is demonstrated that superior accuracy is achievable with all the SANM kernels while the iterative two-node SANM kernel outperforms the others in the multigroup calculations employing more than two groups, and the two-level CMFD formulation is quite efficient in the acceleration of the outer iteration.

https://s-space.snu.ac.kr/bitstream/10371/8784/1/jnst45-668.pdf

B.N. Aviles

Papers

Diffusion theory methods for spatial kinetics calculations

Diffusion theory methods for spatial kinetics calculations