A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a twodimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the "lower level" calculations. At the "higher level" calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time.KEYWORDS: neutron diffusion equation, boundary element method, domain decomposition, Newton's method, block Jacobi method, high order boundary element, non-conforming element, modern nodal method, three dimensional problems, accuracy
A combined method for evaluating the resonance self shielding effect in a two-dimensional power fast reactor fuel assembly is proposed. This method uses the sub-group method to evaluate the self shielding effect of heterogeneous cell and collision probability method in the ultra-fine energy groups to deal with the resonance interference effect between different resonant nuclides.In the present paper, a comparison between the table look-up method and the sub-group method is carried out and it is shown that the latter is superior to the former in a view of evaluating the resonance self shielding effect. These methods have a common defect that it is impossible to treat the resonance interference effect between different resonant nuclides. It can be overcome by using "a correction factor of the resonance interference effect" obtained by the collision probability calculation in the ultra-fine energy groups in a single fuel pin cell model. The microscopic effective cross section obtained by this proposed method agrees well with that by continuous energy Monte Carlo code within 5% relative difference above 100 eV. The k ∞ value is affected about 0.1% k/k by the use of the correction factor. KEYWORDS: power fast reactor fuel assembly, two-dimensional cell model, cell heterogeneity effect, Tone's method, sub-group method, collision probability method, ultra fine energy groups, resonance interference effect
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