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  1. Context. A realistic parametrization of convection and convective boundary mixing in conventional stellar evolution codes is still the subject of ongoing research. To improve the current situation, multidimensional hydrodynamic simulations are used to study convection in stellar interiors. Such simulations are numerically challenging, especially for flows at low Mach numbers which are typical for convection during early evolutionary stages. Aims. We explore the benefits of using a low-Mach hydrodynamic flux solver and demonstrate its usability for simulations in the astrophysical context. Simulations of convection for a realistic stellar profile are analyzed regarding the properties of convective boundary mixing. Methods. The time-implicit Seven-League Hydro (SLH) code was used to perform multidimensional simulations of convective helium shell burning based on a 25  M ⊙ star model. The results obtained with the low-Mach AUSM + -up solver were compared to results when using its non low-Mach variant AUSM B + -up. We applied well-balancing of the gravitational source term to maintain the initial hydrostatic background stratification. The computational grids have resolutions ranging from 180 × 90 2 to 810 × 540 2 cells and the nuclear energy release was boosted by factors of 3 × 10 3 , 1 × 10 4 , and 3 × 10 4 tomore »study the dependence of the results on these parameters. Results. The boosted energy input results in convection at Mach numbers in the range of 10 −3 –10 −2 . Standard mixing-length theory predicts convective velocities of about 1.6 × 10 −4 if no boosting is applied. The simulations with AUSM + -up show a Kolmogorov-like inertial range in the kinetic energy spectrum that extends further toward smaller scales compared with its non low-Mach variant. The kinetic energy dissipation of the AUSM + -up solver already converges at a lower resolution compared to AUSM B + -up. The extracted entrainment rates at the boundaries of the convection zone are well represented by the bulk Richardson entrainment law and the corresponding fitting parameters are in agreement with published results for carbon shell burning. However, our study needs to be validated by simulations at higher resolution. Further, we find that a general increase in the entropy in the convection zone may significantly contribute to the measured entrainment of the top boundary. Conclusion. This study demonstrates the successful application of the AUSM + -up solver to a realistic astrophysical setup. Compressible simulations of convection in early phases at nominal stellar luminosity will benefit from its low-Mach capabilities. Similar to other studies, our extrapolated entrainment rate for the helium-burning shell would lead to an unrealistic growth of the convection zone if it is applied over the lifetime of the zone. Studies at nominal stellar luminosities and different phases of the same convection zone are needed to detect a possible evolution of the entrainment rate and the impact of radiation on convective boundary mixing.« less
  2. Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH , MUSIC , PPMSTAR , PROMPI , and SLH , which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within ≲3 σ of the mean of all simulations on a given grid (128 3 and 256 3 grid cells), where σ describes the statistical variation due to the flow’s time dependence. They also agree well with a 512 3 reference run. The 128 3 and 256 3 simulationsmore »agree within 9% and 4%, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study.« less
    Free, publicly-accessible full text available March 1, 2023