Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions
Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions.
- Research Organization:
- Bettis Atomic Power Lab., West Mifflin, PA (United States)
- Sponsoring Organization:
- USDOE Assistant Secretary for Nuclear Energy, Washington, DC (United States)
- DOE Contract Number:
- AC11-93PN38195
- OSTI ID:
- 527541
- Report Number(s):
- WAPD-T-3133; CONF-971005-2; ON: DE97004551; TRN: 97:018288
- Resource Relation:
- Conference: Joint international conference on mathematical methods and supercomputing in nuclear applications, Saratoga Springs, NY (United States), 6-10 Oct 1997; Other Information: PBD: [1997]
- Country of Publication:
- United States
- Language:
- English
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