Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

This content will become publicly available on Sun Nov 03 00:00:00 EDT 2024

Title: Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

Abstract

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [3]; ORCiD logo [1]; ORCiD logo [4]; ORCiD logo [5]
+ Show Author Affiliations
  1. Rochester Institute of Technology, NY (United States)
  2. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)
  3. Rochester Institute of Technology, NY (United States); NPCx, Estero, FL (United States)
  4. Barcelona Supercomputing Center (BSC) (Spain)
  5. University of Idaho, Moscow, ID (United States); West Virginia University, Morgantown, WV (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); National Aeronautics and Space Administration (NASA); National Science Foundation (NSF)
OSTI Identifier:
2205415
Grant/Contract Number:  
AC05-00OR22725; NASA NNH17ZDA001N-TCAN-17-TCAN17-0018 80NSSC18K1488; ISFM-80NSSC18K0538; PHY-2110338; OAC-2004044/1550436; AST-2009330; OAC-1811228; PHY-1912632; PHY-1806596; PHY-2110352; OAC-2004311; PHY-2018420; PHY-0722703; PHY-1229173; PHY-1726215; OIA-1458952
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. D.
Additional Journal Information:
Journal Volume: 108; Journal Issue: 10; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Classical black holes; General relativity; Neutron stars & pulsars; Numerical relativity; Gravitation, Cosmology & Astrophysics

Citation Formats

Ji, Liwei, Mewes, Vassilios, Zlochower, Yosef, Ennoggi, Lorenzo, Armengol, Federico G. Lopez, Campanelli, Manuela, Cipolletta, Federico, and Etienne, Zachariah B. Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes. United States: N. p., 2023. Web. doi:10.1103/physrevd.108.104005.
Copy to clipboard
Ji, Liwei, Mewes, Vassilios, Zlochower, Yosef, Ennoggi, Lorenzo, Armengol, Federico G. Lopez, Campanelli, Manuela, Cipolletta, Federico, & Etienne, Zachariah B. Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes. United States. https://doi.org/10.1103/physrevd.108.104005
Copy to clipboard
Ji, Liwei, Mewes, Vassilios, Zlochower, Yosef, Ennoggi, Lorenzo, Armengol, Federico G. Lopez, Campanelli, Manuela, Cipolletta, Federico, and Etienne, Zachariah B. Fri . "Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes". United States. https://doi.org/10.1103/physrevd.108.104005.
Copy to clipboard
@article{osti_2205415,
title = {Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes},
author = {Ji, Liwei and Mewes, Vassilios and Zlochower, Yosef and Ennoggi, Lorenzo and Armengol, Federico G. Lopez and Campanelli, Manuela and Cipolletta, Federico and Etienne, Zachariah B.},
abstractNote = {Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.},
doi = {10.1103/physrevd.108.104005},
journal = {Physical Review. D.},
number = 10,
volume = 108,
place = {United States},
year = {Fri Nov 03 00:00:00 EDT 2023},
month = {Fri Nov 03 00:00:00 EDT 2023}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 3, 2024
Publisher's Version of Record
https://doi.org/10.1103/physrevd.108.104005
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Three-dimensional simulations of neutrino-driven core-collapse supernovae from low-mass single and binary star progenitors
journal, January 2019

  • Müller, Bernhard; Tauris, Thomas M.; Heger, Alexander
  • Monthly Notices of the Royal Astronomical Society, Vol. 484, Issue 3
  • DOI: 10.1093/mnras/stz216

A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity
journal, December 2003

Rotating stars in relativity
journal, November 2017

  • Paschalidis, Vasileios; Stergioulas, Nikolaos
  • Living Reviews in Relativity, Vol. 20, Issue 1
  • DOI: 10.1007/s41114-017-0008-x

A Second-Order Godunov Method for Multi-Dimensional Relativistic Magnetohydrodynamics
journal, January 2011

  • Beckwith, Kris; Stone, James M.
  • The Astrophysical Journal Supplement Series, Vol. 193, Issue 1
  • DOI: 10.1088/0067-0049/193/1/6

Merger of black hole-neutron star binaries: Nonspinning black hole case
journal, December 2006

The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics
journal, May 2012

High resolution schemes for hyperbolic conservation laws
journal, March 1983

Time-asymmetric initial data for black holes and black-hole collisions
journal, April 1980

Application of the Cubed-Sphere grid to Tilted Black hole Accretion Disks
journal, January 2009

  • Fragile, P. Chris; Lindner, Christopher C.; Anninos, Peter
  • The Astrophysical Journal, Vol. 691, Issue 1
  • DOI: 10.1088/0004-637X/691/1/482

Circumbinary Magnetohydrodynamic Accretion into Inspiraling Binary Black Holes
journal, July 2012

  • Noble, Scott C.; Mundim, Bruno C.; Nakano, Hiroyuki
  • The Astrophysical Journal, Vol. 755, Issue 1
  • DOI: 10.1088/0004-637X/755/1/51

Shock-avoiding slicing conditions: Tests and calibrations
journal, August 2022

Multi-block simulations in general relativity: high-order discretizations, numerical stability and applications
journal, December 2005

An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows
journal, May 2010

The “Cubed Sphere”: A New Method for the Solution of Partial Differential Equations in Spherical Geometry
journal, March 1996

  • Ronchi, C.; Iacono, R.; Paolucci, P. S.
  • Journal of Computational Physics, Vol. 124, Issue 1
  • DOI: 10.1006/jcph.1996.0047

A fifth-order finite difference scheme for hyperbolic equations on block-adaptive curvilinear grids
journal, January 2016

Efficient implementation of essentially non-oscillatory shock-capturing schemes
journal, August 1988

Optimized High-Order Derivative and Dissipation Operators Satisfying Summation by Parts, and Applications in Three-dimensional Multi-block Evolutions
journal, March 2007

  • Diener, Peter; Dorband, Ernst Nils; Schnetter, Erik
  • Journal of Scientific Computing, Vol. 32, Issue 1
  • DOI: 10.1007/s10915-006-9123-7

Alternatives to standard puncture initial data for binary black hole evolution
journal, September 2012

Accurate Monotonicity-Preserving Schemes with Runge–Kutta Time Stepping
journal, September 1997

Merger and Mass Ejection of Neutron Star Binaries
journal, October 2019

Binary neutron star mergers: a review of Einstein’s richest laboratory
journal, July 2017

Gravitational waves from instabilities in relativistic stars
journal, March 2003

Total variation diminishing Runge-Kutta schemes
journal, January 1998

  • Gottlieb, Sigal; Shu, Chi-Wang
  • Mathematics of Computation of the American Mathematical Society, Vol. 67, Issue 221
  • DOI: 10.1090/S0025-5718-98-00913-2

Smoothing, filtering, and boundary effects
journal, January 1970

Coalescence of black hole–neutron star binaries
journal, December 2021

  • Kyutoku, Koutarou; Shibata, Masaru; Taniguchi, Keisuke
  • Living Reviews in Relativity, Vol. 24, Issue 1
  • DOI: 10.1007/s41114-021-00033-4

Introduction to isolated horizons in numerical relativity
journal, January 2003

Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit
journal, May 2020

Three-dimensional Dynamics of Strongly Twisted Magnetar Magnetospheres: Kinking Flux Tubes and Global Eruptions
journal, April 2023

  • Mahlmann, J. F.; Philippov, A. A.; Mewes, V.
  • The Astrophysical Journal Letters, Vol. 947, Issue 2
  • DOI: 10.3847/2041-8213/accada

Fornax: A Flexible Code for Multiphysics Astrophysical Simulations
journal, February 2019

  • Skinner, M. Aaron; Dolence, Joshua C.; Burrows, Adam
  • The Astrophysical Journal Supplement Series, Vol. 241, Issue 1
  • DOI: 10.3847/1538-4365/ab007f

The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project
journal, August 2019

  • Porth, Oliver; Chatterjee, Koushik; Narayan, Ramesh
  • The Astrophysical Journal Supplement Series, Vol. 243, Issue 2
  • DOI: 10.3847/1538-4365/ab29fd

Accurate Evolutions of Orbiting Black-Hole Binaries without Excision
journal, March 2006

Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes
journal, March 2006

WHAM: a WENO-based general relativistic numerical scheme - I. Hydrodynamics
journal, August 2007

Long-term simulations of multi-dimensional core-collapse supernovae: Implications for neutron star kicks
journal, August 2019

  • Nakamura, Ko; Takiwaki, Tomoya; Kotake, Kei
  • Publications of the Astronomical Society of Japan, Vol. 71, Issue 5
  • DOI: 10.1093/pasj/psz080

Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach
journal, January 2006

  • Anton, Luis; Zanotti, Olindo; Miralles, Juan A.
  • The Astrophysical Journal, Vol. 637, Issue 1
  • DOI: 10.1086/498238

Numerical relativity in spherical coordinates with the Einstein Toolkit
journal, April 2018

Pathologies of hyperbolic gauges in general relativity and other field theories
journal, April 1998

Observation of Gravitational Waves from a Binary Black Hole Merger
journal, February 2016

GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
journal, June 2017

GW170608: Observation of a 19 Solar-mass Binary Black Hole Coalescence
journal, December 2017

An efficient class of WENO schemes with adaptive order
journal, December 2016

  • Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 326
  • DOI: 10.1016/j.jcp.2016.09.009

Stable Characteristic Evolution of Generic Three-Dimensional Single-Black-Hole Spacetimes
journal, May 1998

Improved numerical stability of stationary black hole evolution calculations
journal, October 2002

The Bar‐Mode Instability in Differentially Rotating Neutron Stars: Simulations in Full General Relativity
journal, October 2000

  • Shibata, Masaru; Baumgarte, Thomas W.; Shapiro, Stuart L.
  • The Astrophysical Journal, Vol. 542, Issue 1
  • DOI: 10.1086/309525

Matplotlib: A 2D Graphics Environment
journal, January 2007

Numerical relativity in spherical polar coordinates: Evolution calculations with the BSSN formulation
journal, February 2013

  • Baumgarte, Thomas W.; Montero, Pedro J.; Cordero-Carrión, Isabel
  • Physical Review D, Vol. 87, Issue 4
  • DOI: 10.1103/PhysRevD.87.044026

�ber die partiellen Differenzengleichungen der mathematischen Physik
journal, December 1928

  • Courant, R.; Friedrichs, K.; Lewy, H.
  • Mathematische Annalen, Vol. 100, Issue 1
  • DOI: 10.1007/BF01448839

Multi-messenger Observations of a Binary Neutron Star Merger
journal, October 2017

General relativistic hydrodynamics in curvilinear coordinates
journal, April 2014

High-powered gravitational news
journal, November 1997

The eth formalism in numerical relativity
journal, April 1997

Chimera: A Massively Parallel Code for Core-collapse Supernova Simulations
journal, April 2020

  • Bruenn, Stephen W.; Blondin, John M.; Hix, W. Raphael
  • The Astrophysical Journal Supplement Series, Vol. 248, Issue 1
  • DOI: 10.3847/1538-4365/ab7aff

The Design and Implementation of FFTW3
journal, February 2005

A reduced gravity, primitive equation model of the upper equatorial ocean
journal, April 1989

Evolution of three-dimensional gravitational waves: Harmonic slicing case
journal, November 1995

Numerical relativity in spherical polar coordinates: Off-center simulations
journal, March 2015

Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: Comparison with the BSSN formulation in spherical symmetry
journal, May 2014

Black holes and fundamental fields in numerical relativity: Initial data construction and evolution of bound states
journal, May 2014

On Godunov-Type Methods for Gas Dynamics
journal, April 1988

  • Einfeldt, Bernd
  • SIAM Journal on Numerical Analysis, Vol. 25, Issue 2
  • DOI: 10.1137/0725021

Handing off the outcome of binary neutron star mergers for accurate and long-term postmerger simulations
journal, October 2022

  • Lopez Armengol, Federico G.; Etienne, Zachariah B.; Noble, Scott C.
  • Physical Review D, Vol. 106, Issue 8
  • DOI: 10.1103/PhysRevD.106.083015

A multi-block infrastructure for three-dimensional time-dependent numerical relativity
journal, July 2006

  • Schnetter, Erik; Diener, Peter; Dorband, Ernst Nils
  • Classical and Quantum Gravity, Vol. 23, Issue 16
  • DOI: 10.1088/0264-9381/23/16/S14

Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
journal, January 2003

Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains
journal, January 2008

  • Calhoun, Donna A.; Helzel, Christiane; LeVeque, Randall J.
  • SIAM Review, Vol. 50, Issue 4
  • DOI: 10.1137/060664094

Dynamical bar-mode instability in rotating and magnetized relativistic stars
journal, November 2013

“Yin-Yang grid”: An overset grid in spherical geometry: SPHERICAL OVERSET GRID “YIN-YANG GRID”
journal, September 2004

  • Kageyama, Akira; Sato, Tetsuya
  • Geochemistry, Geophysics, Geosystems, Vol. 5, Issue 9
  • DOI: 10.1029/2004GC000734

Conformal and covariant formulation of the Z4 system with constraint-violation damping
journal, March 2012

Unitarization of gluon distribution in the doubly logarithmic regime at high density
journal, January 1999

Numerical symmetry-preserving techniques for low-dissipation shock-capturing schemes
journal, July 2019

Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics
journal, April 2006

  • Noble, Scott C.; Gammie, Charles F.; McKinney, Jonathan C.
  • The Astrophysical Journal, Vol. 641, Issue 1
  • DOI: 10.1086/500349

Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere
journal, August 2003

  • Du, Qiang; Gunzburger, Max D.; Ju, Lili
  • Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 35-36
  • DOI: 10.1016/S0045-7825(03)00394-3

Black-hole excision with multiple grid patches
journal, July 2004

Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
journal, September 2013

Gauge conditions for long-term numerical black hole evolutions without excision
journal, April 2003

Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach
journal, February 1997

  • Banyuls, Francesc; Font, Jose A.; Ibanez, Jose Ma.
  • The Astrophysical Journal, Vol. 476, Issue 1
  • DOI: 10.1086/303604

The disc-jet symbiosis emerges: modelling the emission of Sagittarius A* with electron thermodynamics
journal, February 2017

  • Ressler, S. M.; Tchekhovskoy, A.; Quataert, E.
  • Monthly Notices of the Royal Astronomical Society, Vol. 467, Issue 3
  • DOI: 10.1093/mnras/stx364

Numerical Relativity and Astrophysics
journal, August 2014

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution
journal, July 1991

  • Balbus, Steven A.; Hawley, John F.
  • The Astrophysical Journal, Vol. 376
  • DOI: 10.1086/170270

Non-linear pulsations in differentially rotating neutron stars: mass-shedding-induced damping and splitting of the fundamental mode
journal, August 2004

  • Stergioulas, Nikolaos; Apostolatos, Theocharis A.; Font, José A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 352, Issue 4
  • DOI: 10.1111/j.1365-2966.2004.07973.x

Numerical relativity of compact binaries in the 21st century
journal, November 2018

The Lazarus project: A pragmatic approach to binary black hole evolutions
journal, January 2002

Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy
journal, May 2000

  • Balsara, Dinshaw S.; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 160, Issue 2
  • DOI: 10.1006/jcph.2000.6443

Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations
journal, June 2015

Kilonovae
journal, December 2019

Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity
journal, May 2006

Neutrino-Driven Supernova of a Low-Mass Iron-Core Progenitor Boosted by Three-Dimensional Turbulent Convection
journal, March 2015

Instability, turbulence, and enhanced transport in accretion disks
journal, January 1998

Magnetized Neutron-Star Mergers and Gravitational-Wave Signals
journal, May 2008

A new general relativistic magnetohydrodynamics code for dynamical spacetimes
journal, October 2008

The Stability of Non-Dissipative Couette flow in Hydromagnetics
journal, February 1960

  • Chandrasekhar, S.
  • Proceedings of the National Academy of Sciences, Vol. 46, Issue 2
  • DOI: 10.1073/pnas.46.2.253

Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
journal, October 2017

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity
journal, June 2007

Accurate simulations of the dynamical bar-mode instability in full general relativity
journal, February 2007

General relativistic simulations of magnetized binary neutron star mergers
journal, July 2008

High accuracy binary black hole simulations with an extended wave zone
journal, February 2011

Are gauge shocks really shocks?
journal, September 2005

Direct Calculation of the Radiative Efficiency of an Accretion disk Around a Black hole
journal, February 2009

Conservative averaging-reconstruction techniques (Ring Average) for 3-D finite-volume MHD solvers with axis singularity
journal, January 2019

  • Zhang, Binzheng; Sorathia, Kareem A.; Lyon, John G.
  • Journal of Computational Physics, Vol. 376
  • DOI: 10.1016/j.jcp.2018.08.020

Neutron Star Mergers and Nucleosynthesis of Heavy Elements
journal, October 2017

GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
journal, October 2017

Stability of general-relativistic accretion disks
journal, February 2011

Horizon pretracking
journal, February 2005

Gravitational waves from neutron star mergers and their relation to the nuclear equation of state
journal, November 2019

Covariant Conservation Laws in General Relativity
journal, February 1959

High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
journal, March 2011

  • Castro, Marcos; Costa, Bruno; Don, Wai Sun
  • Journal of Computational Physics, Vol. 230, Issue 5
  • DOI: 10.1016/j.jcp.2010.11.028

Covariant formulations of Baumgarte, Shapiro, Shibata, and Nakamura and the standard gauge
journal, May 2009

Comparing models of rapidly rotating relativistic stars constructed by two numerical methods
journal, May 1995

  • Stergioulas, Nikolaos; Friedman, John L.
  • The Astrophysical Journal, Vol. 444
  • DOI: 10.1086/175605

Properties of the Binary Black Hole Merger GW150914
journal, June 2016

GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
journal, June 2016

Multipatch methods in general relativistic astrophysics: Hydrodynamical flows on fixed backgrounds
journal, May 2008

The black hole accretion code
journal, May 2017

  • Porth, Oliver; Olivares, Hector; Mizuno, Yosuke
  • Computational Astrophysics and Cosmology, Vol. 4, Issue 1
  • DOI: 10.1186/s40668-017-0020-2

Binary Neutron Star Mergers
journal, July 2012

  • Faber, Joshua A.; Rasio, Frederic A.
  • Living Reviews in Relativity, Vol. 15, Issue 1
  • DOI: 10.12942/lrr-2012-8

PATCHWORK: A Multipatch Infrastructure for Multiphysics/Multiscale/Multiframe Fluid Simulations
journal, June 2018

  • Shiokawa, Hotaka; Cheng, Roseanne M.; Noble, Scott C.
  • The Astrophysical Journal, Vol. 861, Issue 1
  • DOI: 10.3847/1538-4357/aac2dd

Evolution of Binary Black-Hole Spacetimes
journal, September 2005

General relativistic simulations of black-hole–neutron-star mergers: Effects of magnetic fields
journal, March 2012

  • Etienne, Zachariah B.; Liu, Yuk Tung; Paschalidis, Vasileios
  • Physical Review D, Vol. 85, Issue 6
  • DOI: 10.1103/PhysRevD.85.064029

Introduction to dynamical horizons in numerical relativity
journal, July 2006

Maintaining Pressure Positivity in Magnetohydrodynamic Simulations
journal, January 1999

  • Balsara, Dinshaw S.; Spicer, Daniel
  • Journal of Computational Physics, Vol. 148, Issue 1
  • DOI: 10.1006/jcph.1998.6108

Hybrid black-hole binary initial data
journal, June 2011

ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics
journal, July 2007

GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit
journal, November 2013

The dynamics of neutrino-driven supernova explosions after shock revival in 2D and 3D
journal, August 2015

  • Müller, B.
  • Monthly Notices of the Royal Astronomical Society, Vol. 453, Issue 1
  • DOI: 10.1093/mnras/stv1611

A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
journal, January 2002

Spin flips and precession in black-hole-binary mergers
journal, March 2007

Single-domain spectral method for black hole puncture data
journal, September 2004

New Formalism for Numerical Relativity
journal, July 1995

Evolutions in 3D numerical relativity using fixed mesh refinement
journal, February 2004

Mergers of Magnetized Neutron Stars with Spinning Black Holes: Disruption, Accretion, and Fallback
journal, September 2010

SENR / NRPy + : Numerical relativity in singular curvilinear coordinate systems
journal, March 2018

Azimuthal averaging–reconstruction filtering techniques for finite-difference general circulation models in spherical geometry
journal, February 2021

  • Dang, Tong; Zhang, Binzheng; Lei, Jiuhou
  • Geoscientific Model Development, Vol. 14, Issue 2
  • DOI: 10.5194/gmd-14-859-2021

Appearance of coordinate shocks in hyperbolic formalisms of general relativity
journal, May 1997

Formation of precessing jets by tilted black hole discs in 3D general relativistic MHD simulations
journal, October 2017

  • Liska, M.; Hesp, C.; Tchekhovskoy, A.
  • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 474, Issue 1
  • DOI: 10.1093/mnrasl/slx174

GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
journal, October 2017

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: