Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction
Abstract
Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heattransfer applications, a quasisteady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite number of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projectionbased modelreduction approach to make highorder quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (highfidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a highorder quadrature using a reducedorder model constructed from the reducedmore »
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1372351
 Report Number(s):
 SAND20171114J
Journal ID: ISSN 00221481; 650925
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Heat Transfer
 Additional Journal Information:
 Journal Volume: 139; Journal Issue: 12; Journal ID: ISSN 00221481
 Publisher:
 ASME
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; approximation; heat transfer; wavelength; gases; radiation (physics); radiative heat transfer
Citation Formats
Tencer, John, Carlberg, Kevin, Larsen, Marvin, and Hogan, Roy E. Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction. United States: N. p., 2017.
Web. doi:10.1115/1.4037098.
Tencer, John, Carlberg, Kevin, Larsen, Marvin, & Hogan, Roy E. Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction. United States. doi:10.1115/1.4037098.
Tencer, John, Carlberg, Kevin, Larsen, Marvin, and Hogan, Roy E. Sat .
"Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction". United States. doi:10.1115/1.4037098. https://www.osti.gov/servlets/purl/1372351.
@article{osti_1372351,
title = {Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction},
author = {Tencer, John and Carlberg, Kevin and Larsen, Marvin and Hogan, Roy E.},
abstractNote = {Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heattransfer applications, a quasisteady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite number of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projectionbased modelreduction approach to make highorder quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (highfidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a highorder quadrature using a reducedorder model constructed from the reduced basis. Finally, this results in a much more accurate solution than might have been achieved using only the ordinate directions used to compute the reduced basis. One and threedimensional test problems highlight the efficiency of the proposed method.},
doi = {10.1115/1.4037098},
journal = {Journal of Heat Transfer},
number = 12,
volume = 139,
place = {United States},
year = {2017},
month = {6}
}