Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers
Methods. Three such schemes were applied in the implicit, finite-volume Seven-League Hydro code in combination with a lowMach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrod...
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| Main Authors: | , , , , , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
12 August 2021
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| In: |
Astronomy and astrophysics
Year: 2021, Volume: 652, Pages: 1-27 |
| ISSN: | 1432-0746 |
| DOI: | 10.1051/0004-6361/202140653 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1051/0004-6361/202140653 Verlag, lizenzpflichtig, Volltext: https://www.aanda.org/10.1051/0004-6361/202140653 
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| Author Notes: | P.V.F. Edelmann, L. Horst, J.P. Berberich, R. Andrassy, J. Higl, G. Leidi, C. Klingenberg, and F.K. Röpke |
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| 245 | 1 | 0 | |a Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers |c P.V.F. Edelmann, L. Horst, J.P. Berberich, R. Andrassy, J. Higl, G. Leidi, C. Klingenberg, and F.K. Röpke |
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| 520 | |a Methods. Three such schemes were applied in the implicit, finite-volume Seven-League Hydro code in combination with a lowMach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics. - Results. We find that the α-β and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. They accurately conserve minuscule entropy fluctuations advected in an isentropic stratification, which enables the methods to reproduce the expected scaling of convective flow speed with the heating rate. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. The Cargo-LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations. - Conclusions. Overall, we find the well-balanced treatment of gravity in combination with low Mach number flux functions essential to reproducing correct physical solutions to challenging stellar slow-flow problems on affordable collocated grids. | ||
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