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Title: Realizability-preserving DG-IMEX method for the two-moment model of fermion transport

Abstract

Building on the framework of Zhang & Shu [1], [2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f. The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (i.e., f ϵ [0,1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combinedmore » with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and — without interactions with the background — reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. As a result, we also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport.« less

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [2];  [3]
+ Show Author Affiliations
  1. Univ. of Tennessee, Knoxville, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
  3. Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1513400
Alternate Identifier(s):
OSTI ID: 1547579
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 389; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Boltzmann equation; Radiation transport; Hyperbolic conservation laws; Discontinuous Galerkin; Implicit-explicit; Moment realizability

Citation Formats

Chu, Ran, Endeve, Eirik, Hauck, Cory D., and Mezzacappa, Anthony. Realizability-preserving DG-IMEX method for the two-moment model of fermion transport. United States: N. p., 2019. Web. doi:10.1016/j.jcp.2019.03.037.
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Chu, Ran, Endeve, Eirik, Hauck, Cory D., & Mezzacappa, Anthony. Realizability-preserving DG-IMEX method for the two-moment model of fermion transport. United States. https://doi.org/10.1016/j.jcp.2019.03.037
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Chu, Ran, Endeve, Eirik, Hauck, Cory D., and Mezzacappa, Anthony. Wed . "Realizability-preserving DG-IMEX method for the two-moment model of fermion transport". United States. https://doi.org/10.1016/j.jcp.2019.03.037. https://www.osti.gov/servlets/purl/1513400.
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@article{osti_1513400,
title = {Realizability-preserving DG-IMEX method for the two-moment model of fermion transport},
author = {Chu, Ran and Endeve, Eirik and Hauck, Cory D. and Mezzacappa, Anthony},
abstractNote = {Building on the framework of Zhang & Shu [1], [2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f. The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (i.e., f ϵ [0,1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and — without interactions with the background — reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. As a result, we also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport.},
doi = {10.1016/j.jcp.2019.03.037},
journal = {Journal of Computational Physics},
number = C,
volume = 389,
place = {United States},
year = {Wed Mar 27 00:00:00 EDT 2019},
month = {Wed Mar 27 00:00:00 EDT 2019}
}
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