Development of Advanced Nodal Diffusion Methods for Modern Computer Architectures
Rajic, Hrabri Luka
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https://hdl.handle.net/2142/70916
Description
Title
Development of Advanced Nodal Diffusion Methods for Modern Computer Architectures
Author(s)
Rajic, Hrabri Luka
Issue Date
1988
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Engineering, Nuclear
Computer Science
Abstract
A family of highly efficient multidimensional multigroup advanced neutron diffusion nodal methods, ILLICO, have been implemented on sequential, vector, and vector-concurrent computers. Three dimensional realistic benchmark problems can be solved in vectorized mode in less than 0.73 s (33.86 Mflops) on a Cray X-MP/48. Vector-concurrent implementations yield speedups as high as 9.19 on an Alliant FX/8. These results show that the ILLICO method preserves essentially all of its speed advantage (previously demonstrated on scalar computers) over finite difference methods.
A self-consistent higher order nodal diffusion method has been developed and implemented. The method is shown to yield results nearly as accurate (0.02% maximum relative assembly power errors) as those of very fine mesh finite difference methods, using an assembly size coarse mesh. The method was applied to a numerical study of the transverse leakage approximation.
Nodal methods for global nuclear reactor multigroup diffusion calculations which account explicitly for heterogeneities in the assembly nuclear properties have been developed and evaluated. A systematic analysis of the zero order variable cross section nodal method has been conducted. Analyzing the KWU PWR depletion benchmark problem, it is shown that when burnup heterogeneities arise, ordinary nodal methods, which do not explicitly treat the heterogeneities, suffer a significant systematic error that accumulates. It has been recognized that the use of in-node spatially variable material properties is incompatible with the current homogenization methods. A procedure for generating generalized spatially variable nodal cross sections has therefore been devised.
A nodal method which treats explicitly the space dependence of diffusion coefficients has been developed and implemented. It is shown to be effective in problems where very strong heterogeneities occur.
A consistent burnup correction method for nodal microscopic depletion analysis has been developed. The new method makes extremely accurate and computationally highly efficient one node per assembly depletion computations possible. The nodal depletion method is benchmarked on the KWU 2-cycle PWR depletion problem. The results compare very well to the published results obtained with expensive commercially available depletion codes like VENTURE, SIMULATE-3, and NEM-BC.
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