A Higher Harmonics Analysis of 3-D Neutron Diffusion Equation Using the Hierarchical Domain Decomposition Boundary Element Method

摘要

The analysis of higher harmonics of the neutron diffusion equation (NDE)' has become important in many fields of reactor analysis. Conventionally, the higher harmonics have been analyzed based on finite difference approximation by applying the fisson source iteration method (power method) coupled with the subtraction method. The main disadvantage of this method is that the calculation of specific higher harmonics requires information of lower degrees of higher harmonics and their adjoint modes, which increases the computation time and decreases accuracy due to the accumulation of errors in the subtraction process of the higher harmonics. Recently, the boundary element method (BEM) has been applied to solve the NDE. In this application, the NDE is transformed into an equivalent boundary integral equation (BIE). This treatment enables us to evaluate the effect of a boundary easily and rigorously, even if the boundary shape is too complex for the finite difference method (FDM). The BIE needs discretization only on the boundary rather than of the volume, which reduces the number of unknown variables greatly. This becomes especially advantageous in the three dimensional (3-D) analysis. This note presents a new technique for solving the higher harmonics of 3-D NDE with the BEM, based on a hierarchical domain decomposition (HDD) technique. This method can determine higher harmonics and the corresponding eigenvalues directly without the fission source iteration and subtraction process, and with far fewer unknown variables.