Positivity enhancements to the P_{n} transport equations
Abstract
One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). Here, while each solution technique has its disadvantages, in some instances this method can result in oscillations large enough to give a negative radiation energy density, which is nonphysical. Some authors have recast the closure of the transport equations to guarantee positivity. Unfortunately, this results in messy nonlinear equations. Other authors post process each time step’s solution to improve positivity. In this work, the P_{n} equations are modified to be more diffusive, less oscillatory, more positive, and more accurate. No new solution techniques are required, just the scaling of some terms with constant factors and the addition of constant filter opacities; therefore, the solutions are still linear. This new solution method is called stretched and filtered P_{n}. Test problems are presented in one and two dimensions. Comparisons to the D_{n} and TP_{n} closures are made in one dimension. Modifications to D_{n} and TP_{n} are suggested.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1570622
 Report Number(s):
 LAUR1922598
Journal ID: ISSN 23324309
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational and Theoretical Transport
 Additional Journal Information:
 Journal Volume: 48; Journal Issue: 5; Journal ID: ISSN 23324309
 Publisher:
 Taylor and Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Radiation transport; Pn transport; positivity; stretched and filtered Pn
Citation Formats
Olson, Gordon L. Positivity enhancements to the Pn transport equations. United States: N. p., 2019.
Web. doi:10.1080/23324309.2019.1669661.
Olson, Gordon L. Positivity enhancements to the Pn transport equations. United States. doi:10.1080/23324309.2019.1669661.
Olson, Gordon L. Mon .
"Positivity enhancements to the Pn transport equations". United States. doi:10.1080/23324309.2019.1669661. https://www.osti.gov/servlets/purl/1570622.
@article{osti_1570622,
title = {Positivity enhancements to the Pn transport equations},
author = {Olson, Gordon L.},
abstractNote = {One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). Here, while each solution technique has its disadvantages, in some instances this method can result in oscillations large enough to give a negative radiation energy density, which is nonphysical. Some authors have recast the closure of the transport equations to guarantee positivity. Unfortunately, this results in messy nonlinear equations. Other authors post process each time step’s solution to improve positivity. In this work, the Pn equations are modified to be more diffusive, less oscillatory, more positive, and more accurate. No new solution techniques are required, just the scaling of some terms with constant factors and the addition of constant filter opacities; therefore, the solutions are still linear. This new solution method is called stretched and filtered Pn. Test problems are presented in one and two dimensions. Comparisons to the Dn and TPn closures are made in one dimension. Modifications to Dn and TPn are suggested.},
doi = {10.1080/23324309.2019.1669661},
journal = {Journal of Computational and Theoretical Transport},
number = 5,
volume = 48,
place = {United States},
year = {2019},
month = {9}
}
Web of Science
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