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Title: Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes

Abstract

Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.

Authors:
;
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1011140
Report Number(s):
INL/JOU-11-21735
Journal ID: ISSN 0021-9991; TRN: US1102084
DOE Contract Number:  
DE-AC07-05ID14517
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 230; Journal Issue: 3; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; BOLTZMANN EQUATION; DISCRETE ORDINATE METHOD; RADIATION TRANSPORT; ITERATIVE METHODS; MESH GENERATION; adaptive mesh refinement; discontinuous finite element techniques; discrete ordinates method; error estimates; goal-oriented mesh refinement; radiation transport

Citation Formats

Wang, Yaqi, and Ragusa, Jean C. Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes. United States: N. p., 2011. Web. doi:10.1016/j.jcp.2010.10.018.
Wang, Yaqi, & Ragusa, Jean C. Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes. United States. https://doi.org/10.1016/j.jcp.2010.10.018
Wang, Yaqi, and Ragusa, Jean C. 2011. "Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes". United States. https://doi.org/10.1016/j.jcp.2010.10.018.
@article{osti_1011140,
title = {Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes},
author = {Wang, Yaqi and Ragusa, Jean C},
abstractNote = {Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.},
doi = {10.1016/j.jcp.2010.10.018},
url = {https://www.osti.gov/biblio/1011140}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 3,
volume = 230,
place = {United States},
year = {Tue Feb 01 00:00:00 EST 2011},
month = {Tue Feb 01 00:00:00 EST 2011}
}