A Stable, Accurate Methodology for High Mach Number, Strong Magnetic Field MHD Turbulence with Adaptive Mesh Refinement: Resolution and Refinement Studies

TL;DR

This paper presents a robust adaptive mesh refinement methodology for stable, high Mach number MHD turbulence simulations with strong magnetic fields, demonstrating improved stability and consistent turbulence statistics.

Contribution

Develops a new AMR MHD module with advanced schemes ensuring stability for high Mach number turbulence simulations, extending previous capabilities.

Findings

The code remains stable at Mach numbers up to 17.3.

Turbulent dissipation coefficient is approximately 0.5.

Simulation quality correlates with volume-averaged refinement.

Abstract

Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma $\beta_0$ of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers ($M_rms = 17.3$) and smaller plasma beta ($\beta_0 = 0.0067$) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.