COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS
The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basis function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.
- Research Organization:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)
- Sponsoring Organization:
- USDOE Office of Nuclear Energy (NE)
- DOE Contract Number:
- AC07-05ID14517
- OSTI ID:
- 1349203
- Report Number(s):
- INL/CON-16-37891
- Resource Relation:
- Conference: PHYSOR 2016, Sun Valley, ID, 5/1/2016 - 5/5/2016
- Country of Publication:
- United States
- Language:
- English
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