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

Abstract

We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamic (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. Finally, wemore » validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [5]; ORCiD logo [6]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Rochester Inst. of Technology, NY (United States)
  2. Rochester Inst. of Technology, NY (United States)
  3. Bowdoin College, Brunswick, ME (United States)
  4. West Virginia Univ., Morgantown, WV (United States)
  5. Rochester Inst. of Technology, NY (United States); Inst. Argentino de Radioastronomía (IAR), Buenos Aires (Argentina)
  6. Istituto Nazionale di Fisica Nucleare (INFN), Trento (Italy). Trento Inst. for Fundamental Physics and Applications (TIFPA); Univ. di Trento (Italy); Rochester Inst. of Technology, NY (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); National Aeronautics and Space Administration (NASA); Simons Foundation; USDOE Office of Science (SC); Ministry of Economy and Competitiveness (MINECO)
OSTI Identifier:
1617789
Grant/Contract Number:  
AC05-00OR22725; OAC-1550436; AST-1516150; PHY-1607520; PHY-1305730; PHY-1707946; PHY-1726215; PHY-1707526; OIA-1458952; PHY-1806596; ISFM-80NSSC18K0538; TCAN-80NSSC18K1488; 561147; AYA2015-66899-C2-1-P; ACI-1548562; AST-1028087; PHY-0722703; PHY- 1229173
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 101; 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

Citation Formats

Mewes, Vassilios, Zlochower, Yosef, Campanelli, Manuela, Baumgarte, Thomas W., Etienne, Zachariah B., Armengol, Federico G. Lopez, and Cipolletta, Federico. Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.104007.
Mewes, Vassilios, Zlochower, Yosef, Campanelli, Manuela, Baumgarte, Thomas W., Etienne, Zachariah B., Armengol, Federico G. Lopez, & Cipolletta, Federico. Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit. United States. doi:https://doi.org/10.1103/PhysRevD.101.104007
Mewes, Vassilios, Zlochower, Yosef, Campanelli, Manuela, Baumgarte, Thomas W., Etienne, Zachariah B., Armengol, Federico G. Lopez, and Cipolletta, Federico. Tue . "Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit". United States. doi:https://doi.org/10.1103/PhysRevD.101.104007. https://www.osti.gov/servlets/purl/1617789.
@article{osti_1617789,
title = {Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit},
author = {Mewes, Vassilios and Zlochower, Yosef and Campanelli, Manuela and Baumgarte, Thomas W. and Etienne, Zachariah B. and Armengol, Federico G. Lopez and Cipolletta, Federico},
abstractNote = {We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamic (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. Finally, we validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.},
doi = {10.1103/PhysRevD.101.104007},
journal = {Physical Review D},
number = 10,
volume = 101,
place = {United States},
year = {2020},
month = {5}
}

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


Magnetohydrodynamics of Neutrino-Cooled Accretion Tori around a Rotating Black Hole in General Relativity
journal, August 2007

  • Shibata, M.; Sekiguchi, Y. -i.; Takahashi, R.
  • Progress of Theoretical Physics, Vol. 118, Issue 2
  • DOI: 10.1143/PTP.118.257

The multi-messenger picture of compact binary mergers
journal, March 2015


A generalized advection formalism for relativistic fluid simulations
journal, July 2010


High-order fully general-relativistic hydrodynamics: new approaches and tests
journal, March 2014


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

Relativistic Jet Formation from Black Hole Magnetized Accretion Disks: Method, Tests, and Applications of a General RelativisticMagnetohydrodynamic Numerical Code
journal, September 1999

  • Koide, Shinji; Shibata, Kazunari; Kudoh, Takahiro
  • The Astrophysical Journal, Vol. 522, Issue 2
  • DOI: 10.1086/307667

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


New Formalism for Numerical Relativity
journal, July 1995


Binary Black-Hole Mergers in Magnetized Disks: Simulations in Full General Relativity
journal, November 2012


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


Gravitational waves in dynamical spacetimes with matter content in the fully constrained formulation
journal, February 2012

  • Cordero-Carrión, Isabel; Cerdá-Durán, Pablo; Ibáñez, José María
  • Physical Review D, Vol. 85, Issue 4
  • DOI: 10.1103/PhysRevD.85.044023

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


Excision boundary conditions for the conformal metric
journal, November 2008


The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics
journal, September 2005

  • Mignone, A.; Plewa, T.; Bodo, G.
  • The Astrophysical Journal Supplement Series, Vol. 160, Issue 1
  • DOI: 10.1086/430905

Relativistic MHD with adaptive mesh refinement
journal, October 2006

  • Anderson, Matthew; Hirschmann, Eric W.; Liebling, Steven L.
  • Classical and Quantum Gravity, Vol. 23, Issue 22
  • DOI: 10.1088/0264-9381/23/22/025

Systems of conservation laws
journal, May 1960

  • Lax, Peter; Wendroff, Burton
  • Communications on Pure and Applied Mathematics, Vol. 13, Issue 2
  • DOI: 10.1002/cpa.3160130205

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


Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
journal, September 2008


General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code
journal, March 2011


General relativistic magnetohydrodynamic simulations of monopole magnetospheres of black holes
journal, June 2004


General Relativistic Collapse to Black Holes and Gravitational Waves from Black Holes
journal, January 1987

  • Nakamura, Takashi; Oohara, Kenichi; Kojima, Yasufumi
  • Progress of Theoretical Physics Supplement, Vol. 90
  • DOI: 10.1143/PTPS.90.1