- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Constraint damping for the Z4c formulation of general relativity

Andreas Weyhausen, Sebastiano Bernuzzi, and David Hilditch

  • Theoretical Physics Institute, University of Jena, 07743 Jena, Germany

PDF

Phys. Rev. D 85, 024038 – Published 24 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.024038

Abstract

One possibility for avoiding constraint violation in numerical relativity simulations adopting free-evolution schemes is to modify the continuum evolution equations so that constraint violations are damped away. Gundlach et al. demonstrated that such a scheme damps low-amplitude, high-frequency constraint-violating modes exponentially for the Z4 formulation of general relativity. Here we analyze the effect of the damping scheme in numerical applications on a conformal decomposition of Z4. After reproducing the theoretically predicted damping rates of constraint violations in the linear regime, we explore numerical solutions not covered by the theoretical analysis. In particular we examine the effect of the damping scheme on low-frequency and on high-amplitude perturbations of flat spacetime as well and on the long-term dynamics of puncture and compact star initial data in the context of spherical symmetry. We find that the damping scheme is effective provided that the constraint violation is resolved on the numerical grid. On grid noise the combination of artificial dissipation and damping helps to suppress constraint violations. We find that care must be taken in choosing the damping parameter in simulations of puncture black holes. Otherwise the damping scheme can cause undesirable growth of the constraints, and even qualitatively incorrect evolutions. In the numerical evolution of a compact static star we find that the choice of the damping parameter is even more delicate, but may lead to a small decrease of constraint violation. For a large range of values it results in unphysical behavior.

View figure in article

Article Text

References (31)

  1. Othmar Brodbeck, Simonetta Frittelli, Peter Hubner, and Oscar A. Reula, J. Math. Phys. (N.Y.) 40, 909 (1999).
  2. C. Bona, T. Ledvinka, C. Palenzuela, and M. Zacek, Phys. Rev. D 67, 104005 (2003).
  3. C. Bona and C. Palenzuela, Phys. Rev. D 69, 104003 (2004).
  4. C. Bona, T. Ledvinka, C. Palenzuela, and M. Zacek, Phys. Rev. D 69, 064036 (2004).
  5. C. Bona, T. Ledvinka, C. Palenzuela-Luque, and M. Zacek, Classical Quantum Gravity 22, 2615 (2005).
  6. C. Bona and C. Bona-Casas, J. Phys. Conf. Ser. 229, 012022 (2010).
  7. C. Bona and C. Bona-Casas, Phys. Rev. D 82, 064008 (2010).
  8. Carsten Gundlach, Jose M. Martin-Garcia, Gioel Calabrese, and Ian Hinder, Classical Quantum Gravity 22, 3767 (2005).
  9. Frans Pretorius, Phys. Rev. Lett. 95, 121101 (2005).
  10. Sebastiano Bernuzzi and David Hilditch, Phys. Rev. D 81, 084003 (2010).
  11. Milton Ruiz, David Hilditch, and Sebastiano Bernuzzi, Phys. Rev. D 83, 024025 (2011).
  12. Manuela Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006).
  13. John G. Baker, Joan Centrella, Dae-Il Choi, Michael Koppitz, and James van Meter, Phys. Rev. Lett. 96, 111102 (2006).
  14. Daniela Alic, Carles Bona-Casas, Carles Bona, Luciano Rezzolla, and Carlos Palenzuela, arXiv:1106.2254.
  15. Carles Bona, Joan Masso, Edward Seidel, and Joan Stela, Phys. Rev. Lett. 75, 600 (1995).
  16. Miguel Alcubierre et al., Phys. Rev. D 67, 084023 (2003).
  17. Helmut Friedrich, Classical Quantum Gravity 22, L77 (2005).
  18. Milton Ruiz, Oliver Rinne, and Olivier Sarbach, Classical Quantum Gravity 24, 6349 (2007).

  19. We use now the term high not related to the scale ν¯≳1 of the continuum problem, i.e. not for ν∼b, but related to the characteristic frequency introduced by the numerical grid, i.e. ν∼1/h.

  20. B. Gustafsson, H. O. Kreiss, and J. Oliger, Time dependent problems and difference methods (Wiley, New York, 1995).
  21. Steven Brandt and Bernd Bruegmann, Phys. Rev. Lett. 78, 3606 (1997).
  22. J. David Brown, Peter Diener, Olivier Sarbach, Erik Schnetter, and Manuel Tiglio, Phys. Rev. D 79, 044023 (2009).
  23. Mark Hannam, Sascha Husa, Denis Pollney, Bernd Bruegmann, and Niall O’Murchadha, Phys. Rev. Lett. 99, 241102 (2007).
  24. Mark Hannam, Sascha Husa, Frank Ohme, Bernd Bruegmann, and Niall O’Murchadha, Phys. Rev. D 78, 064020 (2008).
  25. David Garfinkle, Carsten Gundlach, and David Hilditch, Classical Quantum Gravity 25, 075007 (2008).
  26. J. David Brown, Phys. Rev. D 77, 044018 (2008).
  27. J. David Brown, Classical Quantum Gravity 25, 205004 (2008).
  28. Marcus Thierfelder, Sebastiano Bernuzzi, David Hilditch, Bernd Brugmann, and Luciano Rezzolla, Phys. Rev. D 83, 064022 (2011).
  29. Marcus Thierfelder, Sebastiano Bernuzzi, and Bernd Bruegmann, Phys. Rev. D 84, 044012 (2011).
  30. Joshua A. Faber, Thomas W. Baumgarte, Zachariah B. Etienne, Stuart L. Shapiro, and Keisuke Taniguchi, Phys. Rev. D 76, 104021 (2007).
  31. J. David Brown et al., Phys. Rev. D 76, 081503 (2007).

Outline

Information

Phys. Rev. D 85, 024038– Published 24 January, 2012
  • Received 28 July 2011

© 2012 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation