A Closed Form Solution for a One-Dimensional Multi-Layered Neutron Transport Problem by Analytical Discrete Ordinates Method

In this work, the Analytical Discrete Ordinates Method (ADO method) is used to provide a closed form solution for a class of one-dimensional neutron transport problems in Cartesian geometry, considering heterogeneous media with linearly anisotropic scattering effects. In this context, the mathematical model will describe a steady-state phenomenon, with neutron sources located inside and on the boundaries of the domain of interest. In the process, the integro-differential transport equation is transformed into an ODE system by the SN angular discretization, which homogeneous solution is obtained with a quadratic eigenvalues problem with reduced order. A particular solution in terms of constants is used. To validate the code, the method and provide benchmark results, test problems will be treated and results will be discussed.