Abstract
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.
Highlights
In recent years, several methods have been proposed with the objective of finding solutions to the equations that model the phenomena of particle transport and radiation [1,2,3,4,5,6]
In this work it was possible to verify the efficiency when the half-range quadrature scheme is associated with Analytical Discrete Ordinates method (ADO) method on the solution of transport problems in homogeneous media, mainly when anisotropy effects are considered
Problems 1 and 2, here described, had already been analyzed using the ADO method, but no study had been done in the sense of verifying the quadrature type influence on the results convergence yet
Summary
Several methods have been proposed with the objective of finding solutions to the equations that model the phenomena of particle transport and radiation [1,2,3,4,5,6]. Maybe the most important has been the Discrete Ordinates method (SN method), which was the first deterministic method to be systematically applied to neutron transport problems [7, 8] with remarkable ability to deal with one-dimensional and multidimensional problems, in different levels of complexity. The limitation of the SN quadrature as to the number of directions (in order to avoid physically unrealistic weighting factors), the difficulties when applied to more complex geometries [12], and the calculation of separation constants bound to the roots of complicated characteristic polynomials, make the use of SN method susceptible to some restrictions or conditions
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