A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors
Abstract
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 ($$\mathscr{M}$$son ≲ 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 $$\mathscr{M}$$son ~ 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.
- Authors:
-
[1];
[2];
[3];
[4];
[3];
[2];
[1]
- Heidelberg Institute for Theoretical Studies (Germany); Heidelberg Univ. (Germany)
- Univ. of Wurzburg (Germany)
- Heidelberg Institute for Theoretical Studies (Germany)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); German Research Foundation (DFG); Klaus Tschira Foundation
- OSTI Identifier:
- 1922024
- Report Number(s):
- LA-UR-22-27864
Journal ID: ISSN 0004-6361; TRN: US2312256
- Grant/Contract Number:
- 89233218CNA000001; RO 3676/3-1; KL 566/22-1
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Astronomy and Astrophysics
- Additional Journal Information:
- Journal Volume: 668; Journal ID: ISSN 0004-6361
- Publisher:
- EDP Sciences
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; hydrodynamics; magnetohydrodynamics (MHD); methods: numerical
Citation Formats
Leidi, Giovanni, Birke, Claudius, Andrassy, Robert, Higl, Johann, Edelmann, Philipp Valentin Ferdinand, Wiest, Gabriel, Klingenberg, Christian, and Röpke, Friedrich K. A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors. United States: N. p., 2022.
Web. doi:10.1051/0004-6361/202244665.
Leidi, Giovanni, Birke, Claudius, Andrassy, Robert, Higl, Johann, Edelmann, Philipp Valentin Ferdinand, Wiest, Gabriel, Klingenberg, Christian, & Röpke, Friedrich K. A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors. United States. https://doi.org/10.1051/0004-6361/202244665
Leidi, Giovanni, Birke, Claudius, Andrassy, Robert, Higl, Johann, Edelmann, Philipp Valentin Ferdinand, Wiest, Gabriel, Klingenberg, Christian, and Röpke, Friedrich K. Mon .
"A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors". United States. https://doi.org/10.1051/0004-6361/202244665. https://www.osti.gov/servlets/purl/1922024.
@article{osti_1922024,
title = {A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors},
author = {Leidi, Giovanni and Birke, Claudius and Andrassy, Robert and Higl, Johann and Edelmann, Philipp Valentin Ferdinand and Wiest, Gabriel and Klingenberg, Christian and Röpke, Friedrich K.},
abstractNote = {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 ($\mathscr{M}$son ≲ 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 $\mathscr{M}$son ~ 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.},
doi = {10.1051/0004-6361/202244665},
journal = {Astronomy and Astrophysics},
number = ,
volume = 668,
place = {United States},
year = {Mon Dec 19 00:00:00 EST 2022},
month = {Mon Dec 19 00:00:00 EST 2022}
}
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