| dc.description.abstract | Simulations for obtaining quantities of interest of neutron transport problems need to be accurate and inexpensive. Discretization in energy has been a historical problem due to the resonances. There are two main approaches for discretization of the energy variables: multigroup (MG) and multiband (MB) methods. However, MG method only converges once resonances are resolved, which requires a large number of energy unknowns. The MB method is not applicable to problems with multiple resonant nuclides in different regions because the band structure becomes multiply defined. Finite-Element-with-Discontiguous-Support (FEDS) method was first proposed by Till[1], and is a novel energy discretization method that is able to capture resonance behavior in the reference solutions with a modest unknown count[1, 2]. The goal of this work is to further improve the FEDS method in order to yield better accuracy with fewer degrees of freedom.
Similar to MB method, FEDS has a discontiguous group structure. However instead of defining the group structure in terms of material total cross section, as in the MB method, the discontiguous group structure in FEDS method is determined by using the hierarchical clustering algorithm to solve a minimization problem on multiple reference solutions. In this way, FEDS method can be applied to problems with multiple resonant nuclides in different areas. In addition, FEDS cross sections have a form that can be accommodated by any standard MG solver.
In this work, the following modifications have been made and tested to the FEDS method: introducing the energy-dependent escape cross section from Monte Carlo (MC); introducing the analytical spatial-dependent escape cross section; implementing the FEDS discontiguous group structure in SERPENT for cross sections weighting.
We tested the NJOY-FEDS method with energy- and space-dependent escape cross sections on a 2D UO2 pin cell problem. We also tested the SERPENT-FEDS method on a 2D UO2 pin cell problem, a 2x2 MOX and UO2 pin cell problem, CASL1B and CASL1E problems. The results are compared to that from a standard MG method and a continuous-energy MC method.
It is observed that introducing the energy-dependent escape cross section improves the NJOY FEDS performance when the number of energy unknowns is small. Introducing the spatial resolution for cross sections in the fuel dramatically improves the accuracy of NJOY-FEDS results. Implementation the FEDS discontiguous group structure in SERPENT for cross sections weighting greatly reduces the error in spatial absorption and fission rate compared to standard SERPENT-MG method. Overall, SERPENT-FEDS cross sections consistently give the best results for keff for all the test problems and always give better performance for power distribution. | en |
