Testing a one-dimensional prescription of dynamical shear mixing with a two-dimensional hydrodynamic simulation

Context. The treatment of mixing processes is still one of the major uncertainties in 1D stellar evolution models. This is mostly due to the need to parametrize and approximate aspects of hydrodynamics in hydrostatic codes. In particular, the effect of hydrodynamic instabilities in rotating stars, for example, dynamical shear instability, evades consistent description. Aims. We intend to study the accuracy of the diffusion approximation to dynamical shear in hydrostatic stellar evolution models by comparing 1D models to a first-principle hydrodynamics simulation starting from the same initial conditions. Methods. We chose an initial model calculated with the stellar evolution code GENEC that is just at the onset of a dynamical shear instability but does not show any other instabilities (e.g., convection). This was mapped to the hydrodynamics code SLH to perform a 2D simulation in the equatorial plane. We compare the resulting profiles in the two codes and compute an effective diffusion coefficient for the hydro simulation. Results. Shear instabilities develop in the 2D simulation in the regions predicted by linear theory to become unstable in the 1D stellar evolution model. Angular velocity and chemical composition is redistributed in the unstable region, thereby creating new unstable regions. After a period of time, the system settles in a symmetric, steady state, which is Richardson stable everywhere in the 2D simulation, whereas the instability remains for longer in the 1D model due to the limitations of the current implementation in the 1D code. A spatially resolved diffusion coefficient is extracted by comparing the initial and final profiles of mean atomic mass. Conclusions. The presented simulation gives a first insight on hydrodynamics of shear instabilities in a real stellar environment and even allows us to directly extract an effective diffusion coefficient. We see evidence for a critical Richardson number of 0.25 as regions above this threshold remain stable for the course of the simulation

Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes

This is the final version. Available from EDP Sciences via the DOI in this recordOur 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 ≲3σ of the mean of all simulations on a given grid (1283 and 2563 grid cells), where σ describes the statistical variation due to the flow’s time dependence. They also agree well with a 5123 reference run. The 1283 and 2563 simulations 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.Science and Technology Facilities Council (STFC)European Research Council (ERC

Three-dimensional Simulations of Massive Stars. I. Wave Generation and Propagation

status: publishe