An Algorithm for Efficient Computation of Multi-layer Neutron Reflection and Transmission Conditions

Presented here is an algorithm for efficient computation of multi-layer neutron reflection and transmission conditions in matrix form. These conditions have been derived from the nodal equations of our hybrid spectral diamond-spectral Green’s function method for one-speed slabgeometry discrete ordinates neutron multiplication eigenvalue problems, and are aimed to replace without spatial truncation error a multi-layered boundary region in spectral nodal reactor computations. In contrast to the independent layer-by-layer algorithm considered thus far in our computations, the algorithm here is based on an inductive approach developed by the present author for deriving neutron reflection and transmission conditions for a boundary region with an arbitrary number of arbitrarily thick layers. With this new algorithm, we increased the computational efficiency of our spectral diamond-spectral Green’s function method for solving neutron multiplication eigenvalue problems with multi-layered boundary regions. We present comparative results for an axial reactor core model to illustrate the increased efficiency of our spectral diamond-spectral Green’s function method, and we close this article with concluding remarks and directions for further research.