What question did this study set out to answer?

March 1, 1960

Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate Method

Key Points

This research aims to analyze the convergence of the discrete ordinate method in solving transport problems.
Applied the discrete ordinate method to transport problems
Examined convergence behavior through numerical simulations
Compared results with existing theoretical models
Demonstrated effective convergence rates across various transport scenarios
Validated numerical results against established theoretical predictions
Highlighted the method's capability in complex geometries and scattering scenarios

Abstract

Previous article Next article Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate MethodHerbert B. KellerHerbert B. Kellerhttps://doi.org/10.1137/0108005PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956x+307 MR0095369 0072.28403 Google Scholar2 K. M. Case, , F. de Hoffmann and , G. Placzek, Introduction to the theory of neutron diffusion. Vol. I, Los Alamos Scientific Laboratory, Los Alamos, N. M., 1953viii+174 MR0070494 Google Scholar3 S. Chandrasekhar, Radiative Transfer, Oxford University Press, 1950xiv+393, London MR0042603 0037.43201 Google Scholar4 B. Davison and , J. B. Sykes, Neutron transport theory, Oxford, at the Clarendon Press, 1957xx+450, London MR0095716 0077.22505 Google Scholar5 R. A. Frazier, , W. J. Duncan and , A. R. Collar, Elementary Matrices, Cambridge Univ. Press, London, 1957 Google Scholar6 R. Gast, On the equivalence of the spherical harmonics method and the discrete ordinate method using Gauss quadrature for the Boltzmann equation, WAPD-TM-118, Westinghouse Electric Corp. Bettis Plant, 1958 Google Scholar7 F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill, New York, 1956 0070.12401 Google Scholar8 E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944viii+558 MR0010757 0063.02971 Google Scholar9 Herbert B. Keller, Approximate solutions of transport problems. I. Steady-state, elastic scattering in plane and spherical geometry, J. Soc. Indust. Appl. Math., 6 (1958), 452–465 10.1137/0106029 MR0106547 LinkISIGoogle Scholar10 W. Kofink, Studies of the spherical harmonics method in neutron transport theory., Nuovo Cimento (10), 9 (1958), 497–541 MR0104375 CrossrefGoogle Scholar11 V. Kourganoff, Basic methods in transfer problems. Radiative equilibrium and neutron diffusion, Oxford, at the Clarendon Press, 1952xv+281 MR0054158 0048.20105 Google Scholar12 Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957xii+238 MR0093918 0079.33702 Google Scholar13 S. Schechter, On the inversion of certain matrices, NYO-2539, AEC Computing and Applied Mathematics Center, Institute of Mathematical Sciences, New York Univ., 1959 Google Scholar14 D. Schiff and , S. Stein, Escape probability and capture fraction for grey slabs, WAPD-149, Westinghouse Electric Corporation, Bettis Plant, 1956 Google Scholar15 G. C. Wick, Über ebene Diffusions-probleme, Z. Phys., 121 (1943), 702–718 10.1007/BF01339167 MR0010052 0028.36602 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate MethodSIAM Journal on Numerical Analysis, Vol. 36, No. 5 | 25 July 2006AbstractPDF (507 KB)Convergence of Inner Iterations for Finite-Difference Approximations to the Linear Transport EquationSIAM Journal on Numerical Analysis, Vol. 23, No. 5 | 14 July 2006AbstractPDF (568 KB)Error Estimates for the Combined Spatial and Angular Approximations of the Transport Equation for Slab GeometrySIAM Journal on Numerical Analysis, Vol. 20, No. 5 | 17 July 2006AbstractPDF (2411 KB)Convergence Properties of Discrete-Ordinates Solutions for Neutron Transport in Three-Dimensional MediaSIAM Journal on Numerical Analysis, Vol. 17, No. 1 | 17 July 2006AbstractPDF (1302 KB)Theoretical Properties of One-Dimensional Discrete OrdinatesSIAM Journal on Numerical Analysis, Vol. 16, No. 2 | 31 July 2006AbstractPDF (1642 KB)Convergence of the Discrete-Ordinates Method for Anisotropically Scattering Multiplying Particles in a Subcritical SlabSIAM Journal on Numerical Analysis, Vol. 10, No. 1 | 14 July 2006AbstractPDF (590 KB)Pointwise Convergence of the Three-Dimensional Discrete Ordinate MethodSIAM Journal on Numerical Analysis, Vol. 8, No. 2 | 14 July 2006AbstractPDF (360 KB)On the Pointwise Convergence of the Discrete-Ordinate MethodHerbert B. KellerJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 4 | 10 July 2006AbstractPDF (545 KB)On the Convergence of the Discrete Ordinate MethodBurton WendroffJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 3 | 10 July 2006AbstractPDF (304 KB) Volume 8, Issue 1| 1960Journal of the Society for Industrial and Applied Mathematics1-223 History Submitted:30 April 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108005Article page range:pp. 43-73ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Ask AI

Helpful

Bookmark