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Title: thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics

Abstract

We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli's exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistics and a convex-invariant time integrator both are demanded. A finite-volume/first-order discontinuous Galerkin(DG) method is used to illustrate how an algebraic moment closure based on Fermi-Dirac statistics is needed to satisfy the bounds. Several algebraic closures are compared with these bounds in mind, and the Cernohorsky and Bludman closure, which satisfies the bounds, is chosen for our IMEX schemes. For the convex-invariant time integrator, two IMEX schemes named PD-ARS have been proposed. PD-ARS denotes a convex-invariant IMEX Runge-Kutta scheme that is high-order accurate in the streaming limit, and works well in the diffusion limit. Our two PD-ARS schemes use second-and third-order, explicit, strong-stability-preserving Runge-Kutta methods as their explicit part, respectively, and therefore are second-and third-order accurate in the streaming limit, respectively. The accuracy and convex-invariance of our PD-ARS schemes are demonstrated in the numerical tests with a third-order DG method for spatial discretization and a simple Lax-Friedrichsmore » flux. The method has been implemented in our high-order neutrino-radiation hydrodynamics (thornado) toolkit. We show preliminary results employing tabulated neutrino opacities.« less

Authors:
 [1]; ORCiD logo [1]; ORCiD logo [1];  [1]; ORCiD logo [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1550754
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Journal Volume: 1225; Conference: ASTRONUM-2018 - Panama City Beach, Florida, United States of America - 6/25/2018 4:00:00 AM-6/29/2018 4:00:00 AM
Country of Publication:
United States
Language:
English

Citation Formats

Chu, Ran, Endeve, Eirik, Hauck, Cory D., Mezzacappa, Anthony, and Messer II, Bronson. thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics. United States: N. p., 2019. Web. doi:10.1088/1742-6596/1225/1/012013.
Chu, Ran, Endeve, Eirik, Hauck, Cory D., Mezzacappa, Anthony, & Messer II, Bronson. thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics. United States. doi:10.1088/1742-6596/1225/1/012013.
Chu, Ran, Endeve, Eirik, Hauck, Cory D., Mezzacappa, Anthony, and Messer II, Bronson. Wed . "thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics". United States. doi:10.1088/1742-6596/1225/1/012013. https://www.osti.gov/servlets/purl/1550754.
@article{osti_1550754,
title = {thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics},
author = {Chu, Ran and Endeve, Eirik and Hauck, Cory D. and Mezzacappa, Anthony and Messer II, Bronson},
abstractNote = {We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli's exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistics and a convex-invariant time integrator both are demanded. A finite-volume/first-order discontinuous Galerkin(DG) method is used to illustrate how an algebraic moment closure based on Fermi-Dirac statistics is needed to satisfy the bounds. Several algebraic closures are compared with these bounds in mind, and the Cernohorsky and Bludman closure, which satisfies the bounds, is chosen for our IMEX schemes. For the convex-invariant time integrator, two IMEX schemes named PD-ARS have been proposed. PD-ARS denotes a convex-invariant IMEX Runge-Kutta scheme that is high-order accurate in the streaming limit, and works well in the diffusion limit. Our two PD-ARS schemes use second-and third-order, explicit, strong-stability-preserving Runge-Kutta methods as their explicit part, respectively, and therefore are second-and third-order accurate in the streaming limit, respectively. The accuracy and convex-invariance of our PD-ARS schemes are demonstrated in the numerical tests with a third-order DG method for spatial discretization and a simple Lax-Friedrichs flux. The method has been implemented in our high-order neutrino-radiation hydrodynamics (thornado) toolkit. We show preliminary results employing tabulated neutrino opacities.},
doi = {10.1088/1742-6596/1225/1/012013},
journal = {},
issn = {1742--6588},
number = ,
volume = 1225,
place = {United States},
year = {2019},
month = {5}
}

Conference:
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