A high-order Godunov scheme for global 3D MHD accretion disks simulations. I. The linear growth regime of the magneto-rotational instability

TL;DR

This paper develops a high-order Godunov scheme with a consistent EMF reconstruction for 3D MHD accretion disk simulations, accurately capturing the linear growth of MRI and avoiding numerical instabilities.

Contribution

It introduces a robust, high-order Godunov scheme with improved EMF reconstruction for stable, accurate 3D MHD accretion disk simulations, validated against analytical MRI growth.

Findings

Reproduced analytical MRI growth rates in 3D simulations.

Identified and mitigated numerical instabilities in the CT method.

Provided a validated code for global 3D accretion disk modeling.

Abstract

We employ the PLUTO code for computational astrophysics to assess and compare the validity of different numerical algorithms on simulations of the magneto-rotational instability in 3D accretion disks. In particular we stress on the importance of using a consistent upwind reconstruction of the electro-motive force (EMF) when using the constrained transport (CT) method to avoid the onset of numerical instabilities. We show that the electro-motive force (EMF) reconstruction in the classical constrained transport (CT) method for Godunov schemes drives a numerical instability. The well-studied linear growth of magneto-rotational instability (MRI) is used as a benchmark for an inter-code comparison of PLUTO and ZeusMP. We reproduce the analytical results for linear MRI growth in 3D global MHD simulations and present a robust and accurate Godunov code which can be used for 3D accretion disk simulations in curvilinear coordinate systems.