Kinematic dynamos and resolution limits for Smoothed Particle Magnetohydrodynamics

TL;DR

This paper investigates the resolution limits of Smoothed Particle Magnetohydrodynamics in simulating magnetic field growth, introducing a new metric to identify and address numerical artefacts in cosmological magnetic field simulations.

Contribution

It presents a novel 'overwinding' trigger metric to determine the resolution and resistivity thresholds needed for accurate MHD simulations using SPH methods.

Findings

Good agreement with reference codes in dynamo tests

Identification of resolution thresholds to prevent numerical artefacts

Application of the metric to cosmological simulations for primordial fields

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 setups 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 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.