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

Chu, Ran; Endeve, Eirik; Hauck, Cory D.; Mezzacappa, Anthony

doi:10.1016/j.jcp.2019.03.037

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

Journal Article · Wed Mar 27 00:00:00 EDT 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.03.037· OSTI ID:1513400

Chu, Ran ^[1];

^[2];

^[2]; Mezzacappa, Anthony ^[3]

Univ. of Tennessee, Knoxville, TN (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1513400

Alternate ID(s):: OSTI ID: 1547579

Journal Information:: Journal of Computational Physics, Vol. 389, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 10 works

Citation information provided by
Web of Science

References (54)

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
On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes Zhang, Xiangxiong; Shu, Chi-Wang Journal of Computational Physics, Vol. 229, Issue 23 https://doi.org/10.1016/j.jcp.2010.08.016	journal	November 2010
Kershaw-type transport equations for fermionic radiation Banach, Zbigniew; Larecki, Wieslaw Zeitschrift für angewandte Mathematik und Physik, Vol. 68, Issue 4 https://doi.org/10.1007/s00033-017-0847-z	journal	August 2017
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
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
The Moment Method in Relativistic Radiative Transfer Anderson, J. L.; Spiegel, E. A. The Astrophysical Journal, Vol. 171 https://doi.org/10.1086/151265	journal	January 1972
Relativistic radiative transfer: moment formalisms Thorne, K. S. Monthly Notices of the Royal Astronomical Society, Vol. 194, Issue 2 https://doi.org/10.1093/mnras/194.2.439	journal	February 1981
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
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
Two-dimensional time dependent Riemann solvers for neutron transport Brunner, Thomas A.; Holloway, James Paul Journal of Computational Physics, Vol. 210, Issue 1 https://doi.org/10.1016/j.jcp.2005.04.011	journal	November 2005
Robust and accurate filtered spherical harmonics expansions for radiative transfer McClarren, Ryan G.; Hauck, Cory D. Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.03.043	journal	August 2010
Implicit filtered P for high-energy density thermal radiation transport using discontinuous Galerkin finite elements Laboure, Vincent M.; McClarren, Ryan G.; Hauck, Cory D. Journal of Computational Physics, Vol. 321 https://doi.org/10.1016/j.jcp.2016.05.046	journal	September 2016
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
Perturbed, entropy-based closure for radiative transfer Frank, Martin; D. Hauck, Cory; Olbrant, Edgar Kinetic & Related Models, Vol. 6, Issue 3 https://doi.org/10.3934/krm.2013.6.557	journal	January 2013
Numerical Methods for Conservation Laws LeVeque, Randall J. Lectures in Mathematics. ETH Zürich https://doi.org/10.1007/978-3-0348-8629-1	book	January 1992
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
Moment closure hierarchies for kinetic theories Levermore, C. David Journal of Statistical Physics, Vol. 83, Issue 5-6 https://doi.org/10.1007/BF02179552	journal	June 1996
Domain of Definition of Levermore's Five-Moment System Junk, Michael Journal of Statistical Physics, Vol. 93, Issue 5/6 https://doi.org/10.1023/B:JOSS.0000033155.07331.d9	journal	December 1998
Convex Duality and Entropy-Based Moment Closures: Characterizing Degenerate Densities Hauck, Cory D.; Levermore, C. David; Tits, André L. SIAM Journal on Control and Optimization, Vol. 47, Issue 4 https://doi.org/10.1137/070691139	journal	January 2008
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
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
Spectral maximum entropy hydrodynamics of fermionic radiation: a three-moment system for one-dimensional flows Banach, Zbigniew; Larecki, Wieslaw Nonlinearity, Vol. 26, Issue 6 https://doi.org/10.1088/0951-7715/26/6/1667	journal	May 2013
Entropy-based mixed three-moment description of fermionic radiation transport in slab and spherical geometries Banach, Zbigniew; Larecki, Wieslaw Kinetic & Related Models, Vol. 10, Issue 4 https://doi.org/10.3934/krm.2017035	journal	January 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
Nodal discontinuous Galerkin methods on graphics processors Klöckner, A.; Warburton, T.; Bridge, J. Journal of Computational Physics, Vol. 228, Issue 21 https://doi.org/10.1016/j.jcp.2009.06.041	journal	November 2009
Formulation of discontinuous Galerkin methods for relativistic astrophysics Teukolsky, Saul A. Journal of Computational Physics, Vol. 312 https://doi.org/10.1016/j.jcp.2016.02.031	journal	May 2016
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
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
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
High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments Shu, Chi-Wang Journal of Computational Physics, Vol. 316 https://doi.org/10.1016/j.jcp.2016.04.030	journal	July 2016
Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations Xing, Yulong; Zhang, Xiangxiong; Shu, Chi-Wang Advances in Water Resources, Vol. 33, Issue 12 https://doi.org/10.1016/j.advwatres.2010.08.005	journal	December 2010
Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms Zhang, Xiangxiong; Shu, Chi-Wang Journal of Computational Physics, Vol. 230, Issue 4 https://doi.org/10.1016/j.jcp.2010.10.036	journal	February 2011
Positivity-preserving DG and central DG methods for ideal MHD equations Cheng, Yue; Li, Fengyan; Qiu, Jianxian Journal of Computational Physics, Vol. 238 https://doi.org/10.1016/j.jcp.2012.12.019	journal	April 2013
Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection–diffusion equations on triangular meshes Zhang, Yifan; Zhang, Xiangxiong; Shu, Chi-Wang Journal of Computational Physics, Vol. 234 https://doi.org/10.1016/j.jcp.2012.09.032	journal	February 2013
Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates Endeve, Eirik; Hauck, Cory D.; Xing, Yulong Journal of Computational Physics, Vol. 287 https://doi.org/10.1016/j.jcp.2015.02.005	journal	April 2015
High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics Wu, Kailiang; Tang, Huazhong Journal of Computational Physics, Vol. 298 https://doi.org/10.1016/j.jcp.2015.06.012	journal	October 2015
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
Strong Stability-Preserving High-Order Time Discretization Methods Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan SIAM Review, Vol. 43, Issue 1 https://doi.org/10.1137/S003614450036757X	journal	January 2001
Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term Chertock, Alina; Cui, Shumo; Kurganov, Alexander SIAM Journal on Numerical Analysis, Vol. 53, Issue 4 https://doi.org/10.1137/151005798	journal	January 2015
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
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
Post-merger evolution of a neutron star-black hole binary with neutrino transport Foucart, Francois; O’Connor, Evan; Roberts, Luke Physical Review D, Vol. 91, Issue 12 https://doi.org/10.1103/PhysRevD.91.124021	journal	June 2015
Hyperbolic character of the angular moment equations of radiative transfer and numerical methods Pons, J. A.; Ibanez, J. M.; Miralles, J. A. Monthly Notices of the Royal Astronomical Society, Vol. 317, Issue 3 https://doi.org/10.1046/j.1365-8711.2000.03679.x	journal	September 2000
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
Analytic closures for M1 neutrino transport Murchikova, E. M.; Abdikamalov, E.; Urbatsch, T. Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 2 https://doi.org/10.1093/mnras/stx986	journal	April 2017
Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations Dimarco, Giacomo; Pareschi, Lorenzo SIAM Journal on Numerical Analysis, Vol. 51, Issue 2 https://doi.org/10.1137/12087606X	journal	January 2013
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms Jin, Shi; Levermore, C. David Journal of Computational Physics, Vol. 126, Issue 2 https://doi.org/10.1006/jcph.1996.0149	journal	July 1996
Semi-implicit time integration for thermal radiative transfer McClarren, Ryan G.; Evans, Thomas M.; Lowrie, Robert B. Journal of Computational Physics, Vol. 227, Issue 16 https://doi.org/10.1016/j.jcp.2008.04.029	journal	August 2008
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
Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I Liu, Xu-Dong; Osher, Stanley SIAM Journal on Numerical Analysis, Vol. 33, Issue 2 https://doi.org/10.1137/0733038	journal	April 1996
Low-storage implicit/explicit Runge–Kutta schemes for the simulation of stiff high-dimensional ODE systems Cavaglieri, Daniele; Bewley, Thomas Journal of Computational Physics, Vol. 286 https://doi.org/10.1016/j.jcp.2015.01.031	journal	April 2015
A TWO-MOMENT RADIATION HYDRODYNAMICS MODULE IN ATHENA USING A TIME-EXPLICIT GODUNOV METHOD Skinner, M. Aaron; Ostriker, Eve C. The Astrophysical Journal Supplement Series, Vol. 206, Issue 2 https://doi.org/10.1088/0067-0049/206/2/21	journal	June 2013
A Comparison of Moment Closures for Linear Kinetic Transport Equations: The Line Source Benchmark Garrett, C. Kristopher; Hauck, Cory D. Transport Theory and Statistical Physics, Vol. 42, Issue 6-7 https://doi.org/10.1080/00411450.2014.910226	journal	September 2013
Conservative 3+1 General Relativistic Variable Eddington Tensor Radiation Transport Equations Cardall, Christian Y.; Endeve, Eirik; Mezzacappa, Anthony arXiv https://doi.org/10.48550/arxiv.1209.2151	text	January 2012

Similar Records

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

Conference · Wed May 01 00:00:00 EDT 2019 · OSTI ID:1513400

Chu, Ran; Endeve, Eirik; Hauck, Cory; +2 more

A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling

Journal Article · Wed Apr 07 00:00:00 EDT 2021 · The Astrophysical Journal. Supplement Series · OSTI ID:1513400

Laiu, M. Paul; Endeve, Eirik; Chu, Ran; +2 more

sta-imex (scripts to investigate stability of IMEX methods)

Software · Mon Apr 06 00:00:00 EDT 2020 · OSTI ID:1513400

Guba, Oksana; Steyer, Andrew

Related Subjects

97 MATHEMATICS AND COMPUTING
Boltzmann equation
Radiation transport
Hyperbolic conservation laws
Discontinuous Galerkin
Implicit-explicit
Moment realizability

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

Citation Formats

References (54)

Similar Records

Related Subjects