Finite element solution of the multi-group neutron diffusion equation applied to the hypothetical core disruptive accident
A two-dimensional (r,z), space-time-energy dependent calculational method has been developed for use in LMFBR hypothetical core disruptive accident (HCDA) analyses which utilizes the Finite Element Method (subsequently referred to as FEM) for the necessary diffusion theory neutronics calculations.The hydrodynamic portion of the calculation is performed with a modified form of the VENUS-I computer program which does a thermodynamic energy balance and uses an energy-density-dependent equation-of-state to calculate the pressures which cause reactor disassembly. The reactivity feedback which results from material motion is based on a Hermite Finite Element neutronics method in (r,z) geometry. The FEM neutronic calculations are done using an Eulerian coordinate system while the VENUS calculations employ a Lagrangian coordinate system. A unique feature of the FEM calculations is that the use of Hermite finite elements allows the analytic construction of iteration matrices. The numerical solution of the resulting system of equations utilizes direct matrix inversion which helps to minimize computing time. The major disadvantage of this method, relative to the standard finite differencing method (FDM), is the additional computational logic which is required. This application of the FEM demonstrates the potential which the method has for providing fast, accurate, and reliable solutions to the multi-group neutron diffusion problem where the effects of local heterogeneities are minimal.
- Research Organization:
- Rensselaer Polytechnic Inst., Troy, NY (USA)
- OSTI ID:
- 5157230
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS
LMFBR TYPE REACTORS
REACTOR CORE DISRUPTION
TWO-DIMENSIONAL CALCULATIONS
COMPUTER-AIDED DESIGN
FINITE ELEMENT METHOD
NEUTRON DIFFUSION EQUATION
NUMERICAL SOLUTION
ACCIDENTS
BREEDER REACTORS
DIFFERENTIAL EQUATIONS
EPITHERMAL REACTORS
EQUATIONS
FAST REACTORS
FBR TYPE REACTORS
LIQUID METAL COOLED REACTORS
REACTOR ACCIDENTS
REACTORS
220900* - Nuclear Reactor Technology- Reactor Safety
210500 - Power Reactors
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