Energy dissipation in astrophysical simulations: results of the Orszag-Tang test problem
Authors
Fatemeh Kayanikhoo, Miljenko Čemeljić, Maciek Wielgus and Włodek Kluźniak
Abstract
The magnetic field through the magnetic reconnection process affects the dynamics and structure of astrophysical systems. Numerical simulations are the tools to study the evolution of these systems. However, the resolution, dimensions, resistivity, and turbulence of the system are some important parameters to take into account in the simulations. In this paper, we investigate the evolution of magnetic energy in astrophysical simulations by performing a standard test problem for MHD codes, Orszag-Tang. We estimate the numerical dissipation in the simulations using state-of-the-art numerical simulation code in astrophysics, PLUTO. The estimated numerical resistivity in 2D simulations corresponds to the Lundquist number ≈ 104 in the resolution of 512 × 512 grid cells. It is also shown that the plasmoid unstable reconnection layer can be resolved with sufficient resolutions. Our analysis demonstrates that in non-relativistic magnetohydrodynamics simulations, magnetic and kinetic energies undergo conversion into internal energy, resulting in plasma heating.
Keywords
Magnetohydrodynamics – magnetic energy dissipation – resistivity – numerical simulations – PLUTO
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References
- Akasofu, S. (1968), Magnetospheric Substorm, pp. 212–253, Springer Netherlands, Dordrecht, ISBN 978-94-010-3461-6.
- Giovanelli, R. G. (1946), A theory of chromospheric flares, Nature Astronomy, 158(4003), pp. 81–82.
- Jiang, X., Chaowei Feng, Liu, R., Yan, X., Hu, Q., Moore, R. L., Duan, A., Cui, J., Zuo, P., Wang, Y. and Wei, F. (2021), A fundamental mechanism of solar eruption initiation, Nature Astronomy, 5, pp. 1126–1138, arXiv: 2107.08204.
- Kayanikhoo, F., Cemeljic, M., Wielgus, M. and Kluzniak, W. (2023), Energy distribution and substructure formation in astrophysical mhd simulations, arXiv: 2308.16062.
- Loureiro, N. F., Schekochihin, A. A. and Cowley, S. C. (2007), Instability of current sheets and formation of plasmoid chains, Physics of Plasmas, 14(10), p. 100703, URL https://doi.org/ 10.10632F1.2783986.
- McPherron, R. L. (1979), Magnetospheric substorms, Reviews of Geophysics, 17(4), pp. 657–681.
- Mignone, A., Bodo, G., Massaglia, S., Matsakos, T., Tesileanu, O., Zanni, C. and Ferrari, A. (2007), Pluto: A numerical code for computational astrophysics, APJS, 170(1), pp. 228–242, arXiv: astro-ph/0701854.
- Orszag, S. A. and Tang, C. M. (1979), Small-scale structure of two-dimensional magnetohydrodynamic turbulence, Journal of Fluid Mechanics, 90, pp. 129–143.
- Puzzoni, E., Mignone, A. and Bodo, G. (2021), On the impact of the numerical method on magnetic reconnection and particle acceleration–i. the mhd case, Monthly Notices of the Royal Astronomical Society, 508(2), pp. 2771–2783.
- Ripperda, B., Bacchini, F. and Philippov, A. A. (2020), Magnetic reconnection and hot spot formation in black hole accretion disks, The Astrophysical Journal, 900(2), p. 100, ISSN 1538-4357.
- Ripperda, B., Liska, M., Chatterjee, K., Musoke, G., Philippov, A. A., Markoff, S. B., Tchekhovskoy, A. and Younsi, Z. (2022), Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection, APJL, 924(2), L32, arXiv: 2109.15115.