Kinematic dynamos and resolution limits for smoothed particle magnetohydrodynamics

Monthly Notices of the Royal Astronomical Society, vol. 541, pp. 3427–3444

Abstract

ABSTRACT Understanding the origin and evolution of magnetic fields on cosmological scales opens up a window into the physics of the early Universe. Numerical simulations of such fields require a careful treatment to faithfully solve the equations of magnetohydrodynamics (MHD) without introducing numerical artefacts. In this paper, we study the growth of the magnetic fields in controlled kinematic dynamo set-ups using both smoothed particle hydrodynamics implementations in the swift code. We assess the quality of the reconstructed solution in the Roberts flow case against the reference implementation in the pencil code and find generally a good agreement. Similarly, we reproduce the known features of the more complex Arnold–Beltrami–Childress (ABC) flow. Using a simple induction-diffusion balance model to analyse the results, we construct an ‘overwinding’ trigger metric to locally detect regions where the magnetic diffusion cannot counteract the expected induction because of limitations in the method’s ability to resolve magnetic field gradients. This metric is then used to identify the necessary resolution and resistivity levels to counteract the overwinding problem. We finally apply this metric to adiabatic cosmological simulations and discuss the resolution requirements needed to resolve the growth of the primordial fields without artefacts.

Authors 5

1. Nikyta Shchutskyi corresponding Aachen Leiden Observatory Lorentz Institute for Theoretical Physics

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University , PO Box 9513, NL-2300 RA Leiden ,

   Lorentz Institute for Theoretical Physics, Leiden University , PO Box 9506, NL-2300 RA Leiden ,

2. Matthieu Schaller Aachen Leiden Observatory Lorentz Institute for Theoretical Physics

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University , PO Box 9513, NL-2300 RA Leiden ,

   Lorentz Institute for Theoretical Physics, Leiden University , PO Box 9506, NL-2300 RA Leiden ,

3. Orestis A. Karapiperis Aachen Leiden Observatory Lorentz Institute for Theoretical Physics

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University , PO Box 9513, NL-2300 RA Leiden ,

   Lorentz Institute for Theoretical Physics, Leiden University , PO Box 9506, NL-2300 RA Leiden ,

4. Federico A. Stasyszyn

   Consejo Nacional de Investigaciones Científicas y Técnicas · Universidad Nacional de Córdoba · Instituto de Astronomía Teórica y Experimental

   Affiliation as printed

   Instituto de Astronomíca Teórica y Experimental (IATE) , CONICET–UNC, Laprida 854, X5000BGR Córdoba ,

   Observatorio Astronómico, Universidad Nacional de Córdoba , Laprida 854, X5000BGR Córdoba ,

5. Axel Brandenburg

   Stockholm University · Ilia State University · AlbaNova · Carnegie Mellon University · KTH Royal Institute of Technology

   Affiliation as printed

   Carnegie Mellon University McWilliams Center for Cosmology, Department of Physics, , PA 15213 Pittsburgh ,

   Nordita, KTH Royal Institute of Technology and Stockholm University , Hannes Alfvéns väg 12, SE-10691 Stockholm ,

   School of Natural Sciences and Medicine, Ilia State University , 3-5 Cholokashvili Avenue, 0194 Tbilisi ,

   Stockholm University The Oskar Klein Centre, Department of Astronomy, , AlbaNova, SE-10691 Stockholm ,