von Neumann Stability Analysis of Braginskii MHD Thermal Conduction, Viscosity, Magnetic Diffusion, and Thermoelectric Effects and an Implementation in Athena++
Abstract
Athena++ is a finite-volume astrophysical magnetohydrodynamics (MHD) code. As of writing, isotropic thermal conduction and kinematic viscosity, Ohmic resistivity, and ambipolar diffusion are present in the main branch. Here we present a fork of Athena++, ``Athena-Aniso''. It implements fully anisotropic thermal conduction (parallel, perpendicular, and the Righi--Leduc effect); anisotropic viscosity (all five Braginskii viscosity tensors); the Hall effect; and several thermoelectric effects (Peltier, Seebeck, Nernst, and Ettingshausen). These effects can be weighted by ionisation fraction in a partially ionised gas, with the neutral part diffusing isotropically. We have also added isotropic bulk viscosity. The Biermann battery is not implemented here. The dissipative terms have super-time-stepping support, while the non-dissipative terms are combined with the ideal MHD flux. A CFL condition for all terms is derived and implemented using von Neumann stability analysis. The dissipative terms are found to be stable under first-order time integration. The non-dissipative terms are found to be stable under third-order time integration. We additionally derive new signal speeds for a modified HLLE Riemann solver. These suppress grid-scale non-linear instabilities still present in the non-dissipative terms. The Nernst/Ettingshausen system is found to be ill-posed unless it is stabilised by both perpendicular thermal conduction and perpendicular magnetic diffusion. We derive a well-posedness criterion for this. We provide numerical tests of each implemented effect against derived analytical solutions.
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BibTeX
@misc{albery2026neumann,
title = {{von Neumann Stability Analysis of Braginskii MHD Thermal Conduction, Viscosity, Magnetic Diffusion, and Thermoelectric Effects and an Implementation in Athena++}},
author = {Alexandra F. Albery and Julian M. Pittard},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05086},
eprint = {2611.05086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - von Neumann Stability Analysis of Braginskii MHD Thermal Conduction, Viscosity, Magnetic Diffusion, and Thermoelectric Effects and an Implementation in Athena++
AU - Alexandra F. Albery
AU - Julian M. Pittard
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05086
UR - https://arxiv.org/abs/2611.05086
AB - Athena++ is a finite-volume astrophysical magnetohydrodynamics (MHD) code. As of writing, isotropic thermal conduction and kinematic viscosity, Ohmic resistivity, and ambipolar diffusion are present in the main branch. Here we present a fork of Athena++, ``Athena-Aniso''. It implements fully anisotropic thermal conduction (parallel, perpendicular, and the Righi--Leduc effect); anisotropic viscosity (all five Braginskii viscosity tensors); the Hall effect; and several thermoelectric effects (Peltier, Seebeck, Nernst, and Ettingshausen). These effects can be weighted by ionisation fraction in a partially ionised gas, with the neutral part diffusing isotropically. We have also added isotropic bulk viscosity. The Biermann battery is not implemented here. The dissipative terms have super-time-stepping support, while the non-dissipative terms are combined with the ideal MHD flux. A CFL condition for all terms is derived and implemented using von Neumann stability analysis. The dissipative terms are found to be stable under first-order time integration. The non-dissipative terms are found to be stable under third-order time integration. We additionally derive new signal speeds for a modified HLLE Riemann solver. These suppress grid-scale non-linear instabilities still present in the non-dissipative terms. The Nernst/Ettingshausen system is found to be ill-posed unless it is stabilised by both perpendicular thermal conduction and perpendicular magnetic diffusion. We derive a well-posedness criterion for this. We provide numerical tests of each implemented effect against derived analytical solutions.
ER -