Implicit filtered PN for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

Vincent M. Laboure; Ryan G. McClarren; Cory D. Hauck

doi:10.1016/j.jcp.2016.05.046

Implicit filtered P_N for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

Vincent M. Laboure
, Ryan G. McClarren
, Cory D. Hauck

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP_N) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

Original language	English
Pages (from-to)	624-643
Number of pages	20
Journal	Journal of Computational Physics
Volume	321
DOIs	https://doi.org/10.1016/j.jcp.2016.05.046
State	Published - Sep 15 2016

Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1217170 and by the U.S. Department of Energy , Office of Science, Office of Advanced Scientific Computing Research. This manuscript has, in part, been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy . The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).

Keywords

Discontinuous Galerkin
Fully implicit methods
Radiation transport
Spectral filtering
Spherical harmonics
Thermal radiative transfer

Access to Document

10.1016/j.jcp.2016.05.046

Cite this

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title = "Implicit filtered PN for high-energy density thermal radiation transport using discontinuous Galerkin finite elements",

abstract = "In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FPN) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.",

keywords = "Discontinuous Galerkin, Fully implicit methods, Radiation transport, Spectral filtering, Spherical harmonics, Thermal radiative transfer",

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AU - Laboure, Vincent M.

AU - McClarren, Ryan G.

AU - Hauck, Cory D.

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Y1 - 2016/9/15

N2 - In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FPN) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

AB - In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FPN) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

KW - Discontinuous Galerkin

KW - Fully implicit methods

KW - Radiation transport

KW - Spectral filtering

KW - Spherical harmonics

KW - Thermal radiative transfer

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