Issue |
A&A
Volume 668, December 2022
|
|
---|---|---|
Article Number | A143 | |
Number of page(s) | 29 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/202244665 | |
Published online | 19 December 2022 |
A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors
1
Heidelberger Institut für Theoretische Studien,
Schloss-Wolfsbrunnenweg 35,
69118
Heidelberg, Germany
e-mail: giovanni.leidi@h-its.org
2
Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut,
Mönchhofstr. 12–14,
69120
Heidelberg, Germany
3
Department of Mathematics, Würzburg University,
Emil-Fischer-Str. 40,
97074
Würzburg, Germany
4
Computer, Computational and Statistical Sciences (CCS) Division and Center for Theoretical Astrophysics (CTA), Los Alamos National Laboratory,
Los Alamos, NM
87545, USA
5
Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik,
Philosophenweg 12,
69120
Heidelberg, Germany
Received:
2
August
2022
Accepted:
18
September
2022
Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such environments are characterized by low (sonic) Mach numbers (ℳson ≲ 10−2). In these regimes, conventional MHD codes typically show excessive dissipation and tend to be inefficient as the Courant–Friedrichs–Lewy (CFL) constraint on the time step becomes too strict. In this work we present a new method for efficiently simulating MHD flows at low Mach numbers in a space-dependent gravitational potential while still retaining all effects of compressibility. The proposed scheme is implemented in the finite-volume SEVEN-LEAGUE HYDRO (SLH) code, and it makes use of a low-Mach version of the five-wave Harten–Lax–van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit–explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically reduces the magnitude of spatial discretization errors in strongly stratified setups. The solenoidal constraint on the magnetic field is enforced by using a constrained transport method on a staggered grid. We carry out five verification tests, including the simulation of a small-scale dynamo in a star-like environment at ℳson ~ 10−3. We demonstrate that the proposed scheme can be used to accurately simulate compressible MHD flows in regimes of low Mach numbers and strongly stratified setups even with moderately coarse grids.
Key words: magnetohydrodynamics (MHD) / methods: numerical
© G. Leidi et al. 2022
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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