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Title: 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 two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.

Authors:
;  [1]; ; ;  [2]
  1. Babcock and Wilcox, Alliance, OH (United States). Research and Development Division
  2. 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):
LBNL-38800; CONF-960815-9
ON: DE96013234; TRN: 96:004616
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Conference
Resource Relation:
Conference: 31. national heat transfer conference, Houston, TX (United States), 3-6 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 two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {3}
}

Conference:
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