On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos

C.J. Nixon, C. C.T. Pringle, J.E. Pringle

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Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma. Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.

Original languageEnglish
Article number905900101
Number of pages20
JournalJournal of Plasma Physics
Issue number1
Early online date5 Jan 2024
Publication statusE-pub ahead of print - 5 Jan 2024

Bibliographical note

Copyright © The Author(s), 2024. Published by Cambridge University Press
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited


This work was supported by the Science and Technology Facilities Council (C.J.N., grant number ST/Y000544/1); and the Leverhulme Trust (C.J.N., grant number RPG-2021-380).


  • astrophysical plasmas

ASJC Scopus subject areas

  • Condensed Matter Physics


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