Finite element methods for space-time reactor analysis
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Finite element methods are developed for the solution of the neutron diffusion equation in space, energy and time domains. Constructions of piecewise polynomial spaces in .multiple variables are considered for the approximation of a general class of piecewise continuous functions such as neutron fluxes and concentrations of nuclear elements. The approximate solution in the piecewise polynomial space is determined by applying the Galerkin scheme to a weak form of the neutron diffusion equation. A piecewise polynomial method is also developed for the solution of first-order ordinary differential equations. The numerical methods are applied to neutron slowing-down problems, static neutron diffusion problems, point kinetics problems and time-dependent neutron diffusion problems. The uniqueness, stability and approximation error of the numerical methods are considered. The finite element methods yield high-order accuracy, depending on the degree of the polynomials used, and thereby permit coarse-mesh calculations. The conventional multigroup method, the Crank-Nicolson and the Pade schemes are shown to be special cases of the finite element methods. Numerical examples are presented which confirm the truncation error and demonstrate the utility of the finite element methods in reactor problems.
- Research Organization:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Organization:
- US Atomic Energy Commission (AEC)
- NSA Number:
- NSA-26-017147
- OSTI ID:
- 4717711
- Report Number(s):
- MIT--3903-5; MITNE--135
- Country of Publication:
- United States
- Language:
- English
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