- Access by Xinjiang University
Characteristic decomposition for relativistic numerical simulations. II. Magnetohydrodynamics
Phys. Rev. D 113, 124016 – Published 8 June, 2026
DOI: https://doi.org/10.1103/g9cn-8kmj
Abstract
The characteristic decomposition for general relativistic magnetohydrodynamics in the comoving frame of the fluid has been known for a long time. However, it has not been known in the coordinate frame of the simulation and in terms of the conserved variables evolved in typical numerical simulations. This paper applies the method of quasi-invertible transformations developed in Paper I to derive this decomposition. Among other benefits, this will allow us to use the most accurate known computational methods, such as full-wave Riemann solvers. The results turn out to be simpler than expected based on earlier attempts.
Physics Subject Headings (PhySH)
See Also
Characteristic decomposition for relativistic numerical simulations. I. Hydrodynamics
Phys. Rev. D 113, 124015 (2026)
Article Text
References (25)
- Y. Bruhat, Etude des equations des fluides chargés relativistes inductifs et conducteurs, Commun. Math. Phys. 3, 334 (1966).
- A. M. Anile and S. Pennisi, On the mathematical structure of test relativistic magnetofluiddynamics, Ann. de l’I.H.P. Phys. théor. 46, 27 (1987), available at http://www.numdam.org/item/AIHPA_1987__46_1_27_0.
- A. M. Anile, Relativistic Fluids and Magneto-Fluids: With Applications in Astrophysics and Plasma Physics (Cambridge University Press, New York, 1989).
- M. H. P. M. van Putten, Maxwell’s equations in divergence form for general media with applications to MHD, Commun. Math. Phys. 141, 63 (1991).
- A. Schoepe, D. Hilditch, and M. Bugner, Revisiting hyperbolicity of relativistic fluids, Phys. Rev. D 97, 123009 (2018).
- J. A. Font, Numerical hydrodynamics and magnetohydrodynamics in general relativity, Living Rev. Relativity 11, 7 (2008).
- P. Mösta, B. C. Mundim, J. A. Faber, R. Haas, S. C. Noble, T. Bode, F. Löffler, C. D. Ott, C. Reisswig, and E. Schnetter, GRHydro: A new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit, Classical Quantum Gravity 31, 015005 (2014).
- S. L. Liebling, L. Lehner, D. Neilsen, and C. Palenzuela, Evolutions of magnetized and rotating neutron stars, Phys. Rev. D 81, 124023 (2010).
- A. J. Penner, General relativistic magnetohydrodynamic Bondi-Hoyle accretion, Mon. Not. R. Astron. Soc. 414, 1467 (2011).
- D. Hilditch and A. Schoepe, Hyperbolicity of divergence cleaning and vector potential formulations of general relativistic magnetohydrodynamics, Phys. Rev. D 99, 104034 (2019).
- S. A. Teukolsky, preceding article, Characteristic decomposition for relativistic numerical simulations: I. Hydrodynamics, Phys. Rev. D 113, 124015 (2026).
- L. Antón, J. A. Miralles, J. M. Martí, J. M. Ibáñez, M. A. Aloy, and P. Mimica, Relativistic magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver, Astrophys. J. Suppl. Ser. 188, 1 (2010).
- J.-M. Ibáñez, I. Cordero-Carrión, M.-Á. Aloy, J.-M. Martí, and J.-A. Miralles, On the convexity of relativistic ideal magnetohydrodynamics, Classical Quantum Gravity 32, 095007 (2015).
- C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).
- L. Antón, Magnetohidrodinámica relativista numérica: Aplicaciones en relatividad especial y general, Ph.D. thesis, Universitat de València, 2008, (in Spanish).
- C. R. Evans and J. F. Hawley, Simulation of magnetohydrodynamic flows: A constrained transport model, Astrophys. J. 332, 659 (1988).
- D. S. Balsara and D. S. Spicer, A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations, J. Comput. Phys. 149, 270 (1999).
- G. Tóth, The constraint in shock-capturing magnetohydrodynamics codes, J. Comput. Phys. 161, 605 (2000).
- N. Deppe, W. Throwe, L. E. Kidder, N. L. Vu, K. C. Nelli, C. Armaza, M. S. Bonilla, F. Hébert, Y. Kim, P. Kumar, G. Lovelace, A. Macedo, J. Moxon, E. O’Shea, H. P. Pfeiffer, M. A. Scheel, S. A. Teukolsky, N. A. Wittek et al., SpECTRE v2025.08.19, 10.5281/zenodo.16906840 (2025).
- R. Donat and A. Marquina, Capturing shock reflections: An improved flux formula, J. Comput. Phys. 125, 42 (1996).
- M. A. Aloy, J. M. Ibáñez, J. M. Martí, and E. Müller, GENESIS: A high-resolution code for three-dimensional relativistic hydrodynamics, Astrophys. J. Suppl. Ser. 122, 151 (1999).
- J. M. Martin-Garcia, xact: Efficient tensor computer algebra, https://josmar493.dreamhosters.com (2025).
- D. Hilditch, Dual foliation formulations of general relativity, arXiv:1509.02071.
- M. A. Scheel, H. P. Pfeiffer, L. Lindblom, L. E. Kidder, O. Rinne, and S. A. Teukolsky, Solving Einstein’s equations with dual coordinate frames, Phys. Rev. D 74, 104006 (2006).
- http://www.black-holes.org/SpEC.html.
