The influence of half-range quadrature scheme on ADO method convergence

In this work, a discrete ordinates solution for a neutron transport problem in one-dimensional Cartesian geometry is presented. In order to evaluate the efficiency of the half-range quadrature scheme, the Analytical Discrete Ordinates method (ADO) is used to solve two classes of problems in finite and homogeneous media (with isotropic and linear anisotropic scattering), for steady-state regime, without inner source and prescribed boundary conditions. Numerical results for the scalar fluxes were obtained and comparisons with other works in the literature were made. The versatility of the use of quadratures has always been seen as an advantage of the ADO method which, besides providing accurate results at a low computational cost, has a simpler approach, allowing the use of free software distribution for the simulations. In the results analysis, it was verified that the use of the half-range quadrature was able to accelerate the convergence, mainly in linearly anisotropic problems.

THE ADO METHOD FOR SOLVING ONE-DIMENSIONAL DEEP-PENETRATION TRANSPORT PROBLEMS

In this work, the Analytical Discrete Ordinate method (ADO method) is used to solve deep-penetration transport problems in one-dimensional Cartesian geometry, subject to isotropic and linear anisotropic scattering effects. The regime is considered permanent, the media are homogeneous, and the fluxes are caused by sources located on the boundaries of the domain. In addition, the energy fluctuations will be considered as not significant, characterizing the phenomena as monoenergetic problems. In order to validate the code, method and provide benchmark results, some test problems will be treated and results will be discussed. In particular, the ADO method generated fairly accurate results when compared to other methods based on SN approaches, at a relatively low computational cost.