The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.
Issue Section:
Radiative Heat Transfer
References
1.
Modest
, M. F.
, 1993
, Radiative Heat Transfer
, McGraw-Hill
, New York
.2.
Siegel
, R.
, and Howell
, J. R.
, 2002
, Thermal Radiation Heat Transfer
, Taylor & Francis
, New York
.3.
Coelho
, P. J.
, 2014
, “Advances in the Discrete Ordinates and Finite Volume Methods for the Solution of Radiative Heat Transfer Problems in Participating Media
,” J. Quant. Spectrosc. Radiat. Transfer
, 145
, pp. 121
–146
.4.
Fiveland
, W. A.
, 1988
, “Three-Dimensional Radiative Heat Transfer Solutions by the Discrete-Ordinates Method
,” J. Thermophys.
, 2
(4
), pp. 309
–316
.5.
Fiveland
, W. A.
, 1984
, “Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures
,” ASME J. Heat Transfer
, 106
(4
), pp. 699
–706
.6.
Fiveland
, W. A.
, 1987
, “Discrete Ordinate Methods for Radiative Heat Transfer in Isotropically and Anisotropically Scattering Media
,” ASME J. Heat Transfer
, 109
(3
), pp. 809
–812
.7.
Morel
, J. E.
, Wareing
, T. A.
, Lowrie
, R. B.
, and Parsons
, D. K.
, 2003
, “Analysis of Ray-Effect Mitigation Techniques
,” Nucl. Sci. Eng.
, 109
(3
), pp. 1
–22
.8.
Coelho
, P. J.
, 2002
, “The Role of Ray Effects and False Scattering on the Accuracy of the Standard and Modified Discrete Ordinates Methods
,” J. Quant. Spectrosc. Radiat. Transfer
, 73
, pp. 231
–238
.9.
Chai
, J. C.
, Lee
, H. S.
, and Patankar
, S. V.
, 1993
, “Ray Effect and False Scattering in the Discrete Ordinates Method
,” Numer. Heat Transfer, Part B
, 24
(4
), pp. 373
–389
.10.
Stone
, J. C.
, 2007
, “Adaptive Discrete-Ordinates Algorithms and Strategies
,” Doctoral dissertation, Texas A&M University, College Station, TX.11.
Brown
, P. N.
, and Chang
, B.
, 2006
, “Locally Refined Quadrature Rules for SN Transport
,” Lawrence Livermore National Laboratory, Livermore, CA, Report No. UCRL-JRNL-220755.12.
Longoni
, G.
, and Haghighhat
, A.
, 2002
, “Development and Application of the Regional Angular Refinement Technique and Its Applications to Non-Conventional Problems
,” Proceedings of PHYSOR, Seoul, Korea, Oct. 7–10.13.
McClarren
, R. G.
, and Ayzman
, Y.
, 2013
, “Improved Discrete Ordinates Solutions Using Angular Filtering
,” 23rd International Conference on Transport Theory
, Santa Fe, NM, Sept. 15–20.14.
Lewis
, E. E.
, and Miller
, W. F.
, Jr., 1993
, Computational Methods of Neutron Transport
, American Nuclear Society
, La Grange Park, IL
.15.
Gast
, R. C.
, 1961
, “The Two-Dimensional Quadruple P0 and P1 Approximations
,” Bettis Atomic Power laboratory, West Mifflin, PA, Report No. WARD-TM-274.16.
Natelson
, M.
, 1971
, “Variational Derivation of Discrete Ordinate-Like Approximations
,” Nucl. Sci. Eng.
, 43
, pp. 131
–144
.17.
Stepanek
, J.
, 1981
, “The DPN and QPN Surface Flux Integral Transport Method in One-Dimensional and X-Y Geometry
,” ANS/ENS International Topical Meeting on Advances in Mathematical Methods for the Solution of Nuclear Engineering Problems
, Munich, Germany, April.18.
Ramankutty
, M. A.
, and Crosbie
, A. L.
, 1998
, “Modified Discrete-Ordinates Solution of Radiative Transfer in Three-Dimensional Rectangular Enclosures
,” J. Quant. Spectrosc. Radiat. Transfer
, 60
(1
), pp. 103
–134
.19.
Koch
, R.
, and Becker
, R.
, 2004
, “Evaluation of Quadrature Schemes for the Discrete Ordinates Method
,” J. Quant. Spectrosc. Radiat. Transfer
, 84
(4
), pp. 423
–435
.20.
Koch
, R.
, Krebs
, W.
, Wittig
, S.
, and Viskanta
, R.
, 1995
, “Discrete Ordinates Quadrature Schemes for Multidimensional Radiative Transfer
,” J. Quant. Spectrosc. Radiat. Transfer
, 53
(4
), pp. 353
–372
. 21.
Rukolaine
, S. A.
, and Yuferev
, V. S.
, 2001
, “Discrete Ordinates Quadrature Schemes Based on the Angular Interpolation of Radiation Intensity
,” J. Quant. Spectrosc. Radiat. Transfer
, 69
(3
), pp. 257
–275
.22.
Fiveland
, W. A.
, and Jessee
, J. P.
, 1996
, “Acceleration Schemes for the Discrete Ordinates Method
,” J. Thermophys. Heat Transfer
, 10
(3
), pp. 445
–451
.23.
Raithby
, G. D.
, and Chui
, E. H.
, 2004
, “Accelerated Solution of the Radiation-Transfer Equation With Strong Scattering
,” J. Thermophys. Heat Transfer
, 18
(4
), pp. 156
–159
.24.
Koo
, H. M.
, Cha
, H.
, and Song
, T. H.
, 2001
, “Convergence Characteristics of Temperature in Radiation Problems
,” Numer. Heat Transfer, Part B
, 40
(4
), pp. 303
–324
.25.
Murthy
, J. Y.
, and Mathur
, S. R.
, 1998
, “Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes
,” J. Thermophys. Heat Transfer
, 12
(3
), pp. 313
–321
.26.
Kang
, S. H.
, and Song
, T. H.
, 2008
, “Finite Element Formulation of the First- and Second-Order Discrete Ordinates Equations for Radiative Heat Transfer Calculation in Three-Dimensional Participating Media
,” J. Quant. Spectrosc. Radiat. Transfer
, 109
(11
), pp. 2094
–2107
.27.
Asllanaj
, F.
, Feldheim
, V.
, and Lybaert
, P.
, 2007
, “Solution of Radiative Heat Transfer in 2-D Geometries by a Modified Finite-Volume Method Based on a Cell Vertex Scheme Using Unstructured Triangular Meshes
,” Numer. Heat Transfer, Part B
, 51
(2
), pp. 97
–119
.28.
Tezduyar
, T. E.
, and Osawa
, Y.
, 2000
, “Finite Element Stabilization Parameters Computed From Element Matrices and Vectors
,” Comput. Methods Appl. Mech. Eng.
, 190
, pp. 411
–430
.29.
Brooks
, A. N.
, and Hughs
, T. J. R.
, 1982
, “Streamline Upwind/Petrov–Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier–Stokes Equations
,” Comp. Methods Appl. Mech. Eng.
, 32
, pp. 199
–259
.30.
Heinrich
, J. C.
, Huyakorn
, P. S.
, Zienkiewicz
, O. C.
, and Mitchell
, A. R.
, 1977
, “An ‘Upwind’ Finite Element Scheme for Two-Dimensional Convective Transport Equation
,” Int. J. Numer. Methods Eng.
, 11
(1
), pp. 131
–143
.31.
Crosbie
, A. L.
, and Schrenker
, R. G.
, 1984
, “Radiative Transfer in a Two-Dimensional Rectangular Medium Exposed to Diffuse Radiation
,” J. Quant. Spectrosc. Radiat. Transfer
, 32
(4
), pp. 339
–372
.32.
Altac
, Z.
, and Tekkalmaz
, M.
, 2004
, “Solution of the Radiative Integral Transfer Equations in Rectangular Participating and Isotropically Scattering Inhomogeneous Medium
,” Int. J. Heat Mass Transfer
, 47
(1
), pp. 101
–109
.33.
Longoni
, G.
, 2004
, “Advanced Quadrature Sets, Acceleration and Preconditioning Techniques for the Discrete Ordinates Method in Parallel Computing Environments
,” Ph.D. dissertation, University of Florida, Gainesville, FL.34.
Carlson
, B. G.
, and Lathrop
, K. D.
, 1968
, “Transport Theory—The Method of Discrete Ordinates
,” Computing Methods in Reactor Physics
, Wiley
, New York
.35.
Carlson
, B. G.
, 1971
, “On a More Precise Definition of Discrete Ordinates Methods
,” Second Conference Transport Theory
, Los Alamos, NM, pp. 348–390.36.
Carlson
, B. G.
, 1970
, “Transport Theory: Discrete Ordinates Quadrature Over the Unit Sphere
,” Los Alamos Scientific Laboratory, Los Alamos, NM.37.
Carlson
, B. G.
, and Lee
, C. E.
, 1961
, “Mechanical Quadrature and the Transport Equation
,” Los Alamos Scientific Laboratory, Los Alamos, NM.38.
Lathrop
, K. D.
, and Carlson
, B. G.
, 1965
“Discrete Ordinates Angular Quadrature of the Neutron Transport Equation
,” Los Alamos Scientific Laboratory, Los Alamos, NM.39.
Lee
, C. E.
, 1962
“Discrete SN Approximation to Transport Theory
,” Los Alamos Scientific Laboratory, Los Alamos, NM.40.
Shoemake
, K.
, 1992
, “Uniform Random Rotations
,” Graphics Gems III
, Academic Press
, London
, pp. 124
–132
.41.
Brannon
, R. M.
, 2002
, “Rotation: A Review of Useful Theorems Involving Proper Orthogonal Matrices Reference to Three-Dimensional Physical Space
,” Sandia National Laboratories, Albuquerque, NM.42.
Howell
, L. H.
, 2002
, “A Discrete Ordinates Algorithm for Radiation Transport Using Block-Structured Adaptive Mesh Refinement
,” Nuclear Explosives Code Development Conference
, Monterey, CA, Oct. 21–24.43.
Howell
, L. H.
, 2004
, “A Parallel AMR Implementation of the Discrete Ordinates Method for Radiation Transport
,” Adaptive Mesh Refinement—Theory and Applications
, Springer
, Berlin
, pp. 255
–270
.44.
Pautz
, S.
, Pandya
, T.
, and Adams
, M.
, 2009
, “Scalable Parallel Prefix Solvers for Discrete Ordinates Transport
,” International Conference on Mathematics, Computational Methods and Reactor Physics
(M&C 2009), Saratoga Springs, New York, May 3–7.45.
Moustafa
, S.
, Dutka-Malen
, I.
, Plagne
, L.
, Poncot
, A.
, and Ramet
, P.
, 2013
, “Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
,” Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo
, Paris, France, Oct. 27–31.46.
Bailey
, T. S.
, and Falgout
, R. D.
, 2009
, “Analysis of Massively Parallel Discrete-Ordinates Transport Sweep Algorithms With Collisions
,” International Conference on Mathematics, Computational Methods, and Reactor Physics
, Saratoga Springs, New York, May 3–7.Copyright © 2016 by ASME
You do not currently have access to this content.