Simulations of astrophysical dynamos

TL;DR

This paper reviews numerical methods and theoretical considerations in simulating astrophysical dynamos, emphasizing the effects of modifications like hyperdiffusion, the use of integral kernels, and the role of magnetic Prandtl number.

Contribution

It introduces and discusses the impact of numerical modifications and theoretical formulations on the accuracy of astrophysical dynamo simulations.

Findings

Numerical modifications can significantly alter dynamo solutions.

Integral kernel formulations are crucial when dynamo growth rates are high.

Magnetic Prandtl number controls energy conversion efficiency.

Abstract

Numerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted.