@inproceedings{abdc4519ca2247baacd69f32a8e3ae36,
title = "Detailed analysis of the asymptotic convergence of the angular discretization error in the uncollided solution to the discrete ordinates transport equation",
abstract = "In this work, the asymptotic convergence of the region-averaged uncollided scalar flux error in the Discrete Ordinates solution to the particle transport equation with increasing quadrature orders is examined. We relate the angular discretization error to the quadrature error, then employ a two-dimensional problem to verify convergence orders for the region-averaged uncollided scalar flux errors. Numerical results show that the angular discretization errors in the region-averaged uncollided scalar flux obtained by Legendre-Chebyshev (LC) class quadratures converge linearly in the reciprocal of the number of discrete ordinates, and the errors obtained by Quadruple Range (QR) class quadratures converge with second order. The different error convergence rates can be estimated by a quadrature error theory based on the regularity of the true solution. Some features encountered in the convergence trend are investigated in detail.",
keywords = "Angular discretization error, Discrete ordinates, Uncollided scalar flux",
author = "Xiaoyu Hu and Azmy, \{Yousry Y.\}",
note = "Publisher Copyright: {\textcopyright} 2019 American Nuclear Society. All rights reserved.; 2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 ; Conference date: 25-08-2019 Through 29-08-2019",
year = "2019",
language = "English (US)",
series = "International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019",
publisher = "American Nuclear Society",
pages = "161--170",
booktitle = "International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019",
address = "United States",
}