An adaptive mesh refinement algorithm for the discrete ordinates method
Abstract
The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in twodimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard singlegrid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard singlegrid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until threedimensional geometries are considered.
 Authors:

 Babcock and Wilcox, Alliance, OH (United States). Research and Development Division
 Lawrence Berkeley National Lab., CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley Lab., CA (United States)
 Sponsoring Org.:
 USDOE, Washington, DC (United States)
 OSTI Identifier:
 272515
 Report Number(s):
 LBNL38800; CONF9608159
ON: DE96013234; TRN: 96:004616
 DOE Contract Number:
 AC0376SF00098
 Resource Type:
 Conference
 Resource Relation:
 Conference: 31. national heat transfer conference, Houston, TX (United States), 36 Aug 1996; Other Information: PBD: Mar 1996
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; MESH GENERATION; ALGORITHMS; RADIANT HEAT TRANSFER; NUMERICAL SOLUTION; CONVERGENCE
Citation Formats
Jessee, J P, Fiveland, W A, Howell, L H, Colella, P, and Pember, R B. An adaptive mesh refinement algorithm for the discrete ordinates method. United States: N. p., 1996.
Web.
Jessee, J P, Fiveland, W A, Howell, L H, Colella, P, & Pember, R B. An adaptive mesh refinement algorithm for the discrete ordinates method. United States.
Jessee, J P, Fiveland, W A, Howell, L H, Colella, P, and Pember, R B. Fri .
"An adaptive mesh refinement algorithm for the discrete ordinates method". United States. https://www.osti.gov/servlets/purl/272515.
@article{osti_272515,
title = {An adaptive mesh refinement algorithm for the discrete ordinates method},
author = {Jessee, J P and Fiveland, W A and Howell, L H and Colella, P and Pember, R B},
abstractNote = {The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in twodimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard singlegrid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard singlegrid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until threedimensional geometries are considered.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {3}
}