Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity

Hunter, Joseph; Endeve, Eirik; Laiu, M. Paul; Xing, Yulong

doi:10.1103/physrevd.111.043001

Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity

Journal Article · Mon Feb 03 00:00:00 EST 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/physrevd.111.043001· OSTI ID:2538323

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The Ohio State Univ., Columbus, OH (United States)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Here we present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2538323

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 111; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (58)

Methods for hyperbolic systems with stiff relaxation Lowrie, R. B.; Morel, J. E. International Journal for Numerical Methods in Fluids, Vol. 40, Issue 3-4 https://doi.org/10.1002/fld.321	journal	January 2002
Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation Pareschi, Lorenzo; Russo, Giovanni Journal of Scientific Computing, Vol. 25, Issue 1 https://doi.org/10.1007/s10915-004-4636-4	journal	October 2005
High Order Asymptotic Preserving Hermite WENO Fast Sweeping Method for the Steady-State $$S_{N}$$ Transport Equations Ren, Yupeng; Xing, Yulong; Wang, Dean Journal of Scientific Computing, Vol. 93, Issue 1 https://doi.org/10.1007/s10915-022-01965-x	journal	August 2022
Kilonovae Metzger, Brian D. Living Reviews in Relativity, Vol. 23, Issue 1 https://doi.org/10.1007/s41114-019-0024-0	journal	December 2019
Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae Mezzacappa, Anthony; Endeve, Eirik; Messer, O. E. Bronson Living Reviews in Computational Astrophysics, Vol. 6, Issue 1 https://doi.org/10.1007/s41115-020-00010-8	journal	November 2020
Neutrino transport in general relativistic neutron star merger simulations Foucart, Francois Living Reviews in Computational Astrophysics, Vol. 9, Issue 1 https://doi.org/10.1007/s41115-023-00016-y	journal	February 2023
Relativistic transport theory Lindquist, Richard W. Annals of Physics, Vol. 37, Issue 3 https://doi.org/10.1016/0003-4916(66)90207-7	journal	May 1966
On third order tensor-valued isotropic functions Pennisi, S. International Journal of Engineering Science, Vol. 30, Issue 5 https://doi.org/10.1016/0020-7225(92)90011-5	journal	May 1992
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes Larsen, Edward W.; Morel, J. E.; Miller, Warren F. Journal of Computational Physics, Vol. 69, Issue 2 https://doi.org/10.1016/0021-9991(87)90170-7	journal	April 1987
Efficient implementation of essentially non-oscillatory shock-capturing schemes Shu, Chi-Wang; Osher, Stanley Journal of Computational Physics, Vol. 77, Issue 2 https://doi.org/10.1016/0021-9991(88)90177-5	journal	August 1988
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II larsen, Edward W.; Morel, J. E. Journal of Computational Physics, Vol. 83, Issue 1 https://doi.org/10.1016/0021-9991(89)90229-5	journal	July 1989
Maximum entropy Eddington factors Minerbo, Gerald N. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 20, Issue 6 https://doi.org/10.1016/0022-4073(78)90024-9	journal	December 1978
Relating Eddington factors to flux limiters Levermore, C. D. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 31, Issue 2 https://doi.org/10.1016/0022-4073(84)90112-2	journal	February 1984
Radiation transfer in the fluid frame: A covariant formulation Munier, Alain; Weaver, Robert Computer Physics Reports, Vol. 3, Issue 3 https://doi.org/10.1016/0167-7977(86)90007-9	journal	April 1986
Radiation transfer in the fluid frame: A covariant formulation Munier, Alain; Weaver, Robert Computer Physics Reports, Vol. 3, Issue 3 https://doi.org/10.1016/0167-7977(86)90008-0	journal	April 1986
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations Ascher, Uri M.; Ruuth, Steven J.; Spiteri, Raymond J. Applied Numerical Mathematics, Vol. 25, Issue 2-3 https://doi.org/10.1016/S0168-9274(97)00056-1	journal	November 1997
On maximum-principle-satisfying high order schemes for scalar conservation laws Zhang, Xiangxiong; Shu, Chi-Wang Journal of Computational Physics, Vol. 229, Issue 9 https://doi.org/10.1016/j.jcp.2009.12.030	journal	May 2010
A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer Olbrant, Edgar; Hauck, Cory D.; Frank, Martin Journal of Computational Physics, Vol. 231, Issue 17 https://doi.org/10.1016/j.jcp.2012.03.002	journal	July 2012
A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations Radice, David; Abdikamalov, Ernazar; Rezzolla, Luciano Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.01.048	journal	June 2013
Realizability-preserving DG-IMEX method for the two-moment model of fermion transport Chu, Ran; Endeve, Eirik; Hauck, Cory D. Journal of Computational Physics, Vol. 389 https://doi.org/10.1016/j.jcp.2019.03.037	journal	July 2019
A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids Bhattacharyya, Maitraya K.; Radice, David Journal of Computational Physics, Vol. 491 https://doi.org/10.1016/j.jcp.2023.112365	journal	October 2023
DG-IMEX method for a two-moment model for radiation transport in the O(v/c) limit Paul Laiu, M.; Endeve, Eirik; Austin Harris, J. Journal of Computational Physics, Vol. 520 https://doi.org/10.1016/j.jcp.2024.113477	journal	January 2025
A numerical model for multigroup radiation hydrodynamics Vaytet, N. M. H.; Audit, E.; Dubroca, B. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 112, Issue 8 https://doi.org/10.1016/j.jqsrt.2011.01.027	journal	May 2011
Entropic derivation of the spectral Eddington factors Larecki, Wieslaw; Banach, Zbigniew Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 112, Issue 15 https://doi.org/10.1016/j.jqsrt.2011.06.011	journal	October 2011
The equilibrium-diffusion limit for radiation hydrodynamics Ferguson, J. M.; Morel, J. E.; Lowrie, R. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 202 https://doi.org/10.1016/j.jqsrt.2017.07.031	journal	November 2017
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems Cockburn, Bernardo; Shu, Chi-Wang Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261 https://doi.org/10.1023/A:1012873910884	journal	September 2001
Fully General Relativistic Simulations of Core-Collapse Supernovae with an Approximate Neutrino Transport Kuroda, Takami; Kotake, Kei; Takiwaki, Tomoya The Astrophysical Journal, Vol. 755, Issue 1 https://doi.org/10.1088/0004-637X/755/1/11	journal	July 2012
Numerical Simulations of Optically Thick Accretion onto a Black Hole. ii. Rotating flow Fragile, P. Chris; Olejar, Ally; Anninos, Peter The Astrophysical Journal, Vol. 796, Issue 1 https://doi.org/10.1088/0004-637X/796/1/22	journal	October 2014
A new Multi-Dimensional General Relativistic Neutrino Hydrodynamic code for Core-Collapse Supernovae. i. Method and code Tests in Spherical Symmetry Müller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald The Astrophysical Journal Supplement Series, Vol. 189, Issue 1 https://doi.org/10.1088/0067-0049/189/1/104	journal	June 2010
Neutrino Transfer in Three Dimensions for Core-Collapse Supernovae. i. Static Configurations Sumiyoshi, K.; Yamada, S. The Astrophysical Journal Supplement Series, Vol. 199, Issue 1 https://doi.org/10.1088/0067-0049/199/1/17	journal	February 2012
Numerical Simulations of Optically Thick Accretion onto a Black Hole. i. Spherical case Fragile, P. Chris; Gillespie, Anna; Monahan, Timothy The Astrophysical Journal Supplement Series, Vol. 201, Issue 2 https://doi.org/10.1088/0067-0049/201/2/9	journal	June 2012
Three-Dimensional Boltzmann Hydro code for core Collapse in Massive Stars. i. Special Relativistic Treatments Nagakura, Hiroki; Sumiyoshi, Kohsuke; Yamada, Shoichi The Astrophysical Journal Supplement Series, Vol. 214, Issue 2 https://doi.org/10.1088/0067-0049/214/2/16	journal	September 2014
A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes O'Connor, Evan; Ott, Christian D. Classical and Quantum Gravity, Vol. 27, Issue 11 https://doi.org/10.1088/0264-9381/27/11/114103	journal	May 2010
Relativistic Hydrodynamics Rezzolla, Luciano; Zanotti, Olindo https://doi.org/10.1093/acprof:oso/9780198528906.001.0001	book	September 2013
Energy conserving and well-balanced discontinuous Galerkin methods for the Euler–Poisson equations in spherical symmetry Zhang, Weijie; Xing, Yulong; Endeve, Eirik Monthly Notices of the Royal Astronomical Society, Vol. 514, Issue 1 https://doi.org/10.1093/mnras/stac1257	journal	May 2022
A new moment-based general-relativistic neutrino-radiation transport code: Methods and first applications to neutron star mergers Radice, David; Bernuzzi, Sebastiano; Perego, Albino Monthly Notices of the Royal Astronomical Society, Vol. 512, Issue 1 https://doi.org/10.1093/mnras/stac589	journal	March 2022
An asymptotically correct implicit–explicit time integration scheme for finite volume radiation-hydrodynamics He, Chong-Chong; Wibking, Benjamin D.; Krumholz, Mark R. Monthly Notices of the Royal Astronomical Society, Vol. 531, Issue 1 https://doi.org/10.1093/mnras/stae1244	journal	May 2024
A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics Just, O.; Obergaulinger, M.; Janka, H. -T. Monthly Notices of the Royal Astronomical Society, Vol. 453, Issue 4 https://doi.org/10.1093/mnras/stv1892	journal	September 2015
Rank-3 moment closures in general relativistic neutrino transport Richers, Sherwood Physical Review D, Vol. 102, Issue 8 https://doi.org/10.1103/PhysRevD.102.083017	journal	October 2020
Robust recovery of primitive variables in relativistic ideal magnetohydrodynamics Kastaun, Wolfgang; Kalinani, Jay Vijay; Ciolfi, Riccardo Physical Review D, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevD.103.023018	journal	January 2021
Conservative formulations of general relativistic kinetic theory Cardall, Christian Y.; Mezzacappa, Anthony Physical Review D, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevD.68.023006	journal	July 2003
Conservative 3 + 1 general relativistic variable Eddington tensor radiation transport equations Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony Physical Review D, Vol. 87, Issue 10 https://doi.org/10.1103/PhysRevD.87.103004	journal	May 2013
Conservative 3 + 1 general relativistic Boltzmann equation Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony Physical Review D, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevD.88.023011	journal	July 2013
Impact of an improved neutrino energy estimate on outflows in neutron star merger simulations Foucart, Francois; O’Connor, Evan; Roberts, Luke Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevD.94.123016	journal	December 2016
Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit Guermond, Jean-Luc; Kanschat, Guido SIAM Journal on Numerical Analysis, Vol. 48, Issue 1 https://doi.org/10.1137/090746938	journal	January 2010
Asymptotic-Preserving and Positivity-Preserving Implicit-Explicit Schemes for the Stiff BGK Equation Hu, Jingwei; Shu, Ruiwen; Zhang, Xiangxiong SIAM Journal on Numerical Analysis, Vol. 56, Issue 2 https://doi.org/10.1137/17M1144362	journal	January 2018
Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity Shibata, M.; Kiuchi, K.; Sekiguchi, Y. -i. Progress of Theoretical Physics, Vol. 125, Issue 6 https://doi.org/10.1143/PTP.125.1255	journal	June 2011
Foundations of Black Hole Accretion Disk Theory Abramowicz, Marek A.; Fragile, P. Chris Living Reviews in Relativity, Vol. 16, Issue 1 https://doi.org/10.12942/lrr-2013-1	journal	January 2013
Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems Adams, Marvin L. Nuclear Science and Engineering, Vol. 137, Issue 3 https://doi.org/10.13182/NSE00-41	journal	March 2001
General-Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae Roberts, Luke F.; Ott, Christian D.; Haas, Roland The Astrophysical Journal, Vol. 831, Issue 1 https://doi.org/10.3847/0004-637X/831/1/98	journal	October 2016
A new Multi-Energy Neutrino Radiation-Hydrodynamics code in full General Relativity and its Application to the Gravitational Collapse of Massive Stars Kuroda, Takami; Takiwaki, Tomoya; Kotake, Kei The Astrophysical Journal Supplement Series, Vol. 222, Issue 2 https://doi.org/10.3847/0067-0049/222/2/20	journal	February 2016
Multi-frequency General Relativistic Radiation-hydrodynamics with M ₁ Closure Anninos, Peter; Fragile, P. Chris The Astrophysical Journal, Vol. 900, Issue 1 https://doi.org/10.3847/1538-4357/abab9c	journal	September 2020
Implementation of Monte Carlo Transport in the General Relativistic SpEC Code Foucart, Francois; Duez, Matthew D.; Hébert, Francois The Astrophysical Journal, Vol. 920, Issue 2 https://doi.org/10.3847/1538-4357/ac1737	journal	October 2021
An Extension of the Athena++ Code Framework for Radiation-magnetohydrodynamics in General Relativity Using a Finite-solid-angle Discretization White, Christopher J.; Mullen, Patrick D.; Jiang 姜, Yan-Fei 燕飞 The Astrophysical Journal, Vol. 949, Issue 2 https://doi.org/10.3847/1538-4357/acc8cf	journal	June 2023
Fornax: A Flexible Code for Multiphysics Astrophysical Simulations Skinner, M. Aaron; Dolence, Joshua C.; Burrows, Adam The Astrophysical Journal Supplement Series, Vol. 241, Issue 1 https://doi.org/10.3847/1538-4365/ab007f	journal	February 2019
ν `bhlight` : Radiation GRMHD for Neutrino-driven Accretion Flows Miller, Jonah M.; Ryan, Ben. R.; Dolence, Joshua C. The Astrophysical Journal Supplement Series, Vol. 241, Issue 2 https://doi.org/10.3847/1538-4365/ab09fc	journal	April 2019
thornado-hydro: A Discontinuous Galerkin Method for Supernova Hydrodynamics with Nuclear Equations of State* Pochik, David; Barker, Brandon L.; Endeve, Eirik The Astrophysical Journal Supplement Series, Vol. 253, Issue 1 https://doi.org/10.3847/1538-4365/abd700	journal	March 2021
General-relativistic Radiation Transport Scheme in Gmunu. I. Implementation of Two-moment-based Multifrequency Radiative Transfer and Code Tests Cheong, Patrick Chi-Kit; Ng, Harry Ho-Yin; Lam, Alan Tsz-Lok The Astrophysical Journal Supplement Series, Vol. 267, Issue 2 https://doi.org/10.3847/1538-4365/acd931	journal	August 2023

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