As a matter of reconstruction -- varying the magnetic Prandtl number in implicit large eddy simulations
Abstract
The magnetic Prandtl number (Pm), the ratio of viscosity to magnetic diffusivity, spans many orders of magnitude in astrophysical plasmas. It shapes how turbulence amplifies and structures magnetic fields. In direct numerical simulations (DNS) the viscosity and magnetic diffusivity can be controlled explicitly and independently, whereas in implicit large eddy simulations (ILES) they are set by the numerical scheme. We test whether, in a finite-volume code, Pm can be varied through the reconstruction scheme by applying different methods to the hydro and magnetic variables. As a proof of concept, we simulate driven, subsonic, homogeneous magnetohydrodynamic turbulence using five pairs of hydrodynamic and magnetic reconstruction schemes at varying resolutions. We measure the effective viscosity and resistivity from the energy transfer between scales. Reconstructing the magnetic field at higher order than the fluid raises the effective magnetic Prandtl number and vice versa. We demonstrate that a mix of second- and third-order reconstruction alone results in a ≳20× change in Pm. A comparison of DNS with matched explicit dissipation at these values agrees with the ILES. Mixed reconstruction thus offers a simple and efficient way to explore Pm not≃ 1 in ILES without adding explicit dissipation.
Related
- Relativistic N-body simulations with mass-varying neutrinos
- Spontaneous wandering of the magnetic axis in pulsars: 3D magneto-thermal simulations and the imprint on braking indices
- Simulations of a Conducting Sphere Moving through Magnetized Plasma II: Effect of Internal Magnetic Fields and Enhancement of Alfvénic Drag
- Low-Mass Magnetic Monopoles in the Galaxy: Simulations and Comparison with Ultra-High-Energy Cosmic-Ray Data
- Magnetic Eruption and Nucleosynthesis in GRνMHD Simulations of Spinning Neutron Star Mergers
BibTeX
@misc{kumar2026matter,
title = {{As a matter of reconstruction -- varying the magnetic Prandtl number in implicit large eddy simulations}},
author = {Vinay Kumar and Philipp Grete},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41493},
eprint = {2610.41493},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41493},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - As a matter of reconstruction -- varying the magnetic Prandtl number in implicit large eddy simulations
AU - Vinay Kumar
AU - Philipp Grete
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41493
UR - https://arxiv.org/abs/2610.41493
AB - The magnetic Prandtl number (Pm), the ratio of viscosity to magnetic diffusivity, spans many orders of magnitude in astrophysical plasmas. It shapes how turbulence amplifies and structures magnetic fields. In direct numerical simulations (DNS) the viscosity and magnetic diffusivity can be controlled explicitly and independently, whereas in implicit large eddy simulations (ILES) they are set by the numerical scheme. We test whether, in a finite-volume code, Pm can be varied through the reconstruction scheme by applying different methods to the hydro and magnetic variables. As a proof of concept, we simulate driven, subsonic, homogeneous magnetohydrodynamic turbulence using five pairs of hydrodynamic and magnetic reconstruction schemes at varying resolutions. We measure the effective viscosity and resistivity from the energy transfer between scales. Reconstructing the magnetic field at higher order than the fluid raises the effective magnetic Prandtl number and vice versa. We demonstrate that a mix of second- and third-order reconstruction alone results in a ≳20× change in Pm. A comparison of DNS with matched explicit dissipation at these values agrees with the ILES. Mixed reconstruction thus offers a simple and efficient way to explore Pm not≃ 1 in ILES without adding explicit dissipation.
ER -