Spatial discretizations for selfadjoint forms of the radiative transfer equations
Abstract
There are three commonly recognized secondorder selfadjoint forms of the neutron transport equation: the evenparity equations, the oddparity equations, and the selfadjoint angular flux equations. Because all of these equations contain secondorder spatial derivatives and are selfadjoint for the monoenergetic case, standard continuous finiteelement discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of timedependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the selfadjoint angular flux equation is referred to as the selfadjoint angular intensity equation. Then we describe a general, arbitraryorder, continuous spatial finiteelement approach that is applied to each of the three equations in conjunction with backwardEuler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the selfadjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes.
 Authors:
 Texas A and M University, Department of Nuclear Engineering, 129 Zachry Engineering Center, College Station, TX 778433133 (United States). Email: morel@tamu.edu
 Computer and Computational Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
 (Korea, Republic of)
 Transpire Technologies, 6659 Kimball Drive, Suite D404, Gig Harbor, Washington 98335 (United States)
 Publication Date:
 OSTI Identifier:
 20767039
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 214; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2005.09.017; PII: S00219991(05)004213; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; EQUATIONS; FINITE ELEMENT METHOD; NEUTRON TRANSPORT THEORY; RADIANT HEAT TRANSFER; THERMAL RADIATION; TIME DEPENDENCE
Citation Formats
Morel, Jim E., Adams, B. Todd, Noh, Taewan, Department of Mathematics, Hongik University, Seoul, McGhee, John M., Evans, Thomas M., and Urbatsch, Todd J.. Spatial discretizations for selfadjoint forms of the radiative transfer equations. United States: N. p., 2006.
Web. doi:10.1016/j.jcp.2005.09.017.
Morel, Jim E., Adams, B. Todd, Noh, Taewan, Department of Mathematics, Hongik University, Seoul, McGhee, John M., Evans, Thomas M., & Urbatsch, Todd J.. Spatial discretizations for selfadjoint forms of the radiative transfer equations. United States. doi:10.1016/j.jcp.2005.09.017.
Morel, Jim E., Adams, B. Todd, Noh, Taewan, Department of Mathematics, Hongik University, Seoul, McGhee, John M., Evans, Thomas M., and Urbatsch, Todd J.. Mon .
"Spatial discretizations for selfadjoint forms of the radiative transfer equations". United States.
doi:10.1016/j.jcp.2005.09.017.
@article{osti_20767039,
title = {Spatial discretizations for selfadjoint forms of the radiative transfer equations},
author = {Morel, Jim E. and Adams, B. Todd and Noh, Taewan and Department of Mathematics, Hongik University, Seoul and McGhee, John M. and Evans, Thomas M. and Urbatsch, Todd J.},
abstractNote = {There are three commonly recognized secondorder selfadjoint forms of the neutron transport equation: the evenparity equations, the oddparity equations, and the selfadjoint angular flux equations. Because all of these equations contain secondorder spatial derivatives and are selfadjoint for the monoenergetic case, standard continuous finiteelement discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of timedependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the selfadjoint angular flux equation is referred to as the selfadjoint angular intensity equation. Then we describe a general, arbitraryorder, continuous spatial finiteelement approach that is applied to each of the three equations in conjunction with backwardEuler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the selfadjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes.},
doi = {10.1016/j.jcp.2005.09.017},
journal = {Journal of Computational Physics},
number = 1,
volume = 214,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2006},
month = {Mon May 01 00:00:00 EDT 2006}
}

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Periodic differential equations with selfadjoint monodromy operator
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