Recent Studies on the Asymptotic Convergence of the Spatial Discretization for Two-Dimensional Discrete Ordinates Solutions

Barichello, L. B.; Tres, A.; Picoloto, C. B.; Azmy, Y. Y.

doi:10.1080/23324309.2016.1171242

Recent Studies on the Asymptotic Convergence of the Spatial Discretization for Two-Dimensional Discrete Ordinates Solutions

Journal Article · Wed Jul 13 00:00:00 EDT 2016 · Journal of Computational and Theoretical Transport

DOI:https://doi.org/10.1080/23324309.2016.1171242· OSTI ID:1437435

Barichello, L. B. ^[1]; Tres, A. ^[2]; Picoloto, C. B. ^[2]; Azmy, Y. Y. ^[3]

Universidade Federal do Rio Grande do Sul, Porto Alegre (Brazil). Instituto de Matemática e Estatística; North Carolina State University
Universidade Federal do Rio Grande do Sul, Porto Alegre (Brazil). Instituto de Matemática e Estatística
North Carolina State Univ., Raleigh, NC (United States). Department of Nuclear Engineering

In this paper, four types of quadrature schemes are used to define discrete directions in the solution of a two-dimensional fixed-source discrete ordinates problem in Cartesian geometry. Such schemes enable generating numerical results for averaged scalar fluxes over specified regions of the domain with high number (up to 105) of directions per octant. Two different nodal approaches, the ADO and AHOT-N0 methods, are utilized to obtain the numerical results of interest. The AHOT-N0 solutions on a sequence of refined meshes are then used to develop an asymptotic analysis of the spatial discretization error in order to derive a reference solution. It was more clearly observed that the spatial discretization error converges asymptotically with second order for the source region with all four quadratures employed, while for the other regions refined meshes along with tighter convergence criterion must be applied to evidence the same behavior. Although, in that case, some differences among the four quadrature schemes results were found.

Research Organization:: North Carolina State University, Raleigh, NC (United States). Consortium for Nonproliferation Enabling Capabilities (CNEC)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)

Grant/Contract Number:: NA0002576

OSTI ID:: 1437435

Journal Information:: Journal of Computational and Theoretical Transport, Journal Name: Journal of Computational and Theoretical Transport Journal Issue: 4 Vol. 45; ISSN 2332-4309

Publisher:: Taylor and FrancisCopyright Statement

Country of Publication:: United States

Language:: English

References (9)

Arbitrarily high order characteristic methods for solving the neutron transport equation Azmy, Yousry Y. Annals of Nuclear Energy, Vol. 19, Issue 10-12 https://doi.org/10.1016/0306-4549(92)90004-U	journal	October 1992
A discrete-ordinates solution for a non-grey model with complete frequency redistribution Barichello, L. B.; Siewert, C. E. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 62, Issue 6 https://doi.org/10.1016/S0022-4073(98)00096-X	journal	August 1999
A posteriori error estimator and AMR for discrete ordinates nodal transport methods Duo, Jose I.; Azmy, Yousry Y.; Zikatanov, Ludmil T. Annals of Nuclear Energy, Vol. 36, Issue 3 https://doi.org/10.1016/j.anucene.2008.12.008	journal	April 2009
An analytical approach for a nodal scheme of two-dimensional neutron transport problems Barichello, L. B.; Cabrera, L. C.; Prolo Filho, J. F. Annals of Nuclear Energy, Vol. 38, Issue 6 https://doi.org/10.1016/j.anucene.2011.02.004	journal	June 2011
Angular Quadratures for Improved Transport Computations Abu-Shumays, I. K. Transport Theory and Statistical Physics, Vol. 30, Issue 2-3 https://doi.org/10.1081/TT-100105367	journal	June 2001
Lagrange Discrete Ordinates: A New Angular Discretization for the Three-Dimensional Linear Boltzmann Equation Ahrens, Cory D. Nuclear Science and Engineering, Vol. 180, Issue 3 https://doi.org/10.13182/NSE14-76	journal	July 2015
Compatible Product Angular Quadrature for Neutron Transport in x-y Geometry Abu-Shumays, I. K. Nuclear Science and Engineering, Vol. 64, Issue 2 https://doi.org/10.13182/NSE64-299	journal	October 1977
Finite Element Solutions of the Neutron Transport Equation with Applications to Strong Heterogeneities Martin, William R.; Duderstadt, James J. Nuclear Science and Engineering, Vol. 62, Issue 3 https://doi.org/10.13182/NSE77-A26979	journal	March 1977
Explicit formulation of a nodal transport method for discrete ordinates calculations in two-dimensional fixed-source problems Tres, A.; Picoloto, C. B.; Filho, J. F. Prolo Kerntechnik, Vol. 79, Issue 2 https://doi.org/10.3139/124.110413	journal	April 2014