Mitigating numerical dissipation in simulations of subsonic turbulent flows

TL;DR

This paper introduces a new numerical scheme, USM-BK, for simulating subsonic MHD turbulence, which reduces dissipation and improves accuracy over conventional methods, enabling better resolution of small-scale structures.

Contribution

The paper presents USM-BK, a novel numerical scheme that minimizes dissipation and enhances accuracy in low-Mach MHD turbulence simulations, outperforming existing schemes.

Findings

USM-BK reduces energy dissipation compared to other schemes.

USM-BK constrains magnetic divergence close to machine precision.

USM-BK achieves higher Reynolds numbers and better resolves small-scale structures.

Abstract

Magnetohydrodynamic (MHD) simulations of subsonic (Mach number~$<1$) turbulence are crucial to our understanding of several processes including oceanic and atmospheric flows, the amplification of magnetic fields in the early universe, accretion discs, and stratified flows in stars. In this work, we demonstrate that conventional numerical schemes are excessively dissipative in this low-Mach regime. We demonstrate that a new numerical scheme (termed `USM-BK' and implemented in the FLASH MHD code) reduces the dissipation of kinetic and magnetic energy, constrains the divergence of magnetic field to zero close to machine precision, and resolves smaller-scale structure than other, more conventional schemes, and hence, is the most accurate for simulations of low-Mach turbulent flows among the schemes compared in this work. We first compare several numerical schemes/solvers, including Split-Roe, Split-Bouchut, USM-Roe, USM-HLLC, USM-HLLD, and the new USM-BK, on a simple vortex problem. We then compare the schemes/solvers in simulations of the turbulent dynamo and show that the choice of scheme affects the growth rate, saturation level, and viscous and resistive dissipation scale of the dynamo. We also measure the numerical kinematic Reynolds number (Re) and magnetic Reynolds number (Rm) of our otherwise ideal MHD flows, and show that the new USM-BK scheme provides the highest Re and comparable Rm amongst all the schemes compared.