A Discrete Generalized Multigroup Energy Expansion Theory

This study describes the generalized multigroup energy treatment for the neutron transport equation. Discrete Legendre orthogonal polynomials (DLOPs) are used to expand the energy dependence of the angular flux into a set of flux moments. The leading (zeroth)-order equation is identical to a standard multigroup solution, while the higher-order equations are decoupled from each other and only depend on the leading-order solution because of the orthogonality property of the DLOPs. This decoupling leads to computational times comparable to the coarse-group calculation but provides an accurate fine-group energy spectrum. One-dimensional single-assembly and core calculations were performed to demonstrate the potential of the discrete generalized multigroup method. Computational results show that the discrete generalized multigroup method can produce an accurate fine-group whole-core solution for less computational time. A source update process is also introduced that provides improvement of integral quantities such as eigenvalue and reaction rates over the coarse-group solution.