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Title: Positivity enhancements to the Pn 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 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.

Authors:
 [1]
  1. 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):
LA-UR-19-22598
Journal ID: ISSN 2332-4309
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Theoretical Transport
Additional Journal Information:
Journal Name: Journal of Computational and Theoretical Transport; Journal ID: ISSN 2332-4309
Publisher:
Taylor and Francis
Country of Publication:
United States
Language:
English
Subject:
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.
@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 = ,
volume = ,
place = {United States},
year = {2019},
month = {9}
}

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Works referenced in this record:

Positive $P_N$ Closures
journal, January 2010

  • Hauck, Cory; McClarren, Ryan
  • SIAM Journal on Scientific Computing, Vol. 32, Issue 5
  • DOI: 10.1137/090764918

Implicit filtered P for high-energy density thermal radiation transport using discontinuous Galerkin finite elements
journal, September 2016

  • Laboure, Vincent M.; McClarren, Ryan G.; Hauck, Cory D.
  • Journal of Computational Physics, Vol. 321
  • DOI: 10.1016/j.jcp.2016.05.046

Positivity Limiters for Filtered Spectral Approximations of Linear Kinetic Transport Equations
journal, August 2018


Robust and accurate filtered spherical harmonics expansions for radiative transfer
journal, August 2010


On solutions to the Pn equations for thermal radiative transfer
journal, February 2008

  • McClarren, Ryan G.; Holloway, James Paul; Brunner, Thomas A.
  • Journal of Computational Physics, Vol. 227, Issue 5
  • DOI: 10.1016/j.jcp.2007.11.027

Second-order time evolution of PN equations for radiation transport
journal, May 2009


Alternate closures for radiation transport using Legendre polynomials in 1D and spherical harmonics in 2D
journal, April 2012


Diffusion, P1, and other approximate forms of radiation transport
journal, March 2000

  • Olson, Gordon L.; Auer, Lawrence H.; Hall, Michael L.
  • Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 64, Issue 6
  • DOI: 10.1016/S0022-4073(99)00150-8

Diffusive Corrections to $P_N$ Approximations
journal, January 2011

  • Schäfer, Matthias; Frank, Martin; Levermore, C. David
  • Multiscale Modeling & Simulation, Vol. 9, Issue 1
  • DOI: 10.1137/090764542

Optimal prediction for moment models: crescendo diffusion and reordered equations
journal, July 2009


Moment closures based on minimizing the residual of the P angular expansion in radiation transport
journal, June 2016