Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers - Edelmann, Philipp V. F.; Horst, Leonhard; Berberich, J. P.; Andrássy, Róbert; Higl, Johann; Leidi, Giovanni; Klingenberg, C.; Röpke, Friedrich (Astronomy and astrophysics, 2021)
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.