A multi-level surface rebalancing approach for efficient convergence acceleration of 3D full core multi-group fine grid nodal diffusion iterations

A new multi-level surface rebalancing (MLSR) approach has been developed, aimed at enabling an improved non-linear acceleration of nodal flux iteration convergence in 3D steady-state and transient reactor simulation. This development is meant specifically for anticipating computational needs for solving envisaged multi-group diffusion-like SPN calculations with enhanced mesh resolution (i.e. 3D multi-box up to 3D pin-by-pin grid). For the latter grid refinement regime, the previously available multi-level coarse mesh rebalancing (MLCMR) strategy has been observed to become increasingly inefficient with increasing 3D mesh resolution. Furthermore, for very fine 3D grids that feature a very fine axial mesh as well, non-convergence phenomena have been observed to emerge. In the verifications pursued up to now, these problems have been resolved by the new approach. The novelty arises from taking the interface current balance equations defined over all Cartesian box edges, instead of the nodal volume-integrated process-rate balance equation, as an appropriate restriction basis for setting up multi-level acceleration of fine grid interface current iterations. The new restriction strategy calls for the use of a newly derived set of adjoint spectral equations that are needed for computing a limited set of spectral response vectors per node. This enables a straightforward determination of group-condensed interface current spectral coupling operators that are of crucial relevance in the new rebalancing setup. Another novelty in the approach is a new variational method for computing the neutronic eigenvalue. Within this context, the latter is treated as a control parameter for driving another, newly defined and numerically more fundamental eigenvalue to unity. This paper presents a rigorous derivation of the new approach, followed by a comparison on convergence efficiencies, for a number of 3D full core nodal grid resolution regimes, between the previously available multi-level rebalancing setup and the new multi-level surface rebalancing concept. The surface rebalancing methodology and a number of related concepts are covered in the patents EP2091049, EP2287855, EP2287854 and EP2287853 that were granted in 2012.