Improved Discrete Ordinates Calculations for an Approximate Model of Neutral Particle Transport in Ducts

Improvements in the ADO Method for a One-Dimensional Model of Neutral Particle Transport in Ducts

“…In our previous work (Garcia, 2013), the ADO method introduced by Barichello and Siewert (1999) in the field of radiative transfer was used to solve a discrete ordinates version of Equation (1), that is…”

“…, N. Equation (4) was obtained by employing two separate (but symmetrical) quadrature schemes of order N in the negative and positive ranges of the angular variable ξ . The quadrature nodes and weights for integration in ξ ∈ (0, ∞) are denoted, respectively, by {ξ n } and {w n }, and are defined as in Garcia (2013) by mapping the standard Gauss-Legendre nodes {μ n } and weights {v n } from (−1, 1) into (0, ∞), according to a transformation suggested by Gautschi (1968), viz.…”

“…Numerical results reported in that work (Garcia, 2013) show that the ADO method is much more efficient than previously used numerical implementations of the discrete-ordinates method (Larsen et al, 1986;Garcia et al, 2000). In this work, we discuss some improvements that make the developed ADO method (Garcia, 2013) more consistent from a mathematical point of view.…”

“…After the averaging process described in detail by Prinja and Pomraning (1984) is carried out and a change of variables is introduced as discussed by those authors, we obtain a 1D transport equation that can be written as (Garcia, 2013) …”

“…Very recently (Garcia, 2013), we have successfully adapted the analytical discrete-ordinates (ADO) method of Barichello and Siewert (1999) for treating the PP model. Numerical results reported in that work (Garcia, 2013) show that the ADO method is much more efficient than previously used numerical implementations of the discrete-ordinates method (Larsen et al, 1986;Garcia et al, 2000).…”