Application of the ADO method on disadvantage-factor calculation for heterogeneous slab cells considering linear anisotropic scattering effects

Abstract

In this work, the disadvantage-factor calculation is performed by a version of the Analytical Discrete Ordinates method (ADO method). For this, a class of one-dimenisional neutron transport problems in Cartesian geometry, with linearly anisotropic scattering effects in layered heterogeneous media, will be considered. The process consists in applying the angular discretization S_N, converting the integro-differential transport equation into an ordinary differential equations system, which homogeneous solution is obtained by a quadratic eigenvalues problem with reduced order. To establish a closed form solution for this class of problems, particular solutions in terms of constants are used, as well as reflective boundary conditions and interface conditions. In order to validate the code, the method and to provide benchmark results, a class of two-layered problems is treated. A brief discussion on the influence of anisotropy is made and numerical aspects are discussed.