Spatial recondensation using the Discrete Generalized Multigroup method

Cross-section recondensation using the Discrete Generalized Multigroup method (DGM) has shown promise in improving coarse group solutions by capturing neighboring spectral effects. However, full consistency with the fine group is only assured when using a spatially flat angular flux approximation, such as used in step difference discrete ordinates. Moving to high order spatial methods, such as characteristic type methods, reveals spatial inconsistencies that exist between the DGM equations and the original fine group equations. We propose two methods to address the spatial inconsistencies between DGM and the fine group equations. The first method introduces local spatial dependence of the angular and scalar fluxes, determined using higher order spatial methods, into the cross section moments and del terms defined in DGM. This provides much better agreement between the DGM solution and the fine group solution for any high order spatial method. Unfortunately, this process introduces significant increases to the required memory storage. This issue can be mitigated to some extent through replacement of storage with on-the-fly calculations and a procedure to do so is outlined as well. The second method defines an exact del term by applying the spatial method to the fine group equations before deriving the DGM equations. This new definition allows for convergence to the exact fine group solution. While these equations need to be built specifically for a given spatial method and still suffer from large storage requirements, higher order spatial methods are no longer required and introducing physics informed approximations should significantly reduce the memory burden.