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Register a new userHydrodynamic simulations of H entrainment at the top of He-shell flash convection
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We present the first 3-dimensional, fully compressible gas-dynamics simulations in $4pi$ geometry of He-shell flash convection with proton-rich fuel entrainment at the upper boundary. This work is motivated by the insufficiently understood observed consequences of the H-ingestion flash in post-AGB stars (Sakurais object) and metal-poor AGB stars. Our investigation is focused on the entrainment process at the top convection boundary and on the subsequent advection of H-rich material into deeper layers, and we therefore ignore the burning of the proton-rich fuel in this study. We find that, for our deep convection zone, coherent convective motions of near global scale appear to dominate the flow. At the top boundary convective shear flows are stable against Kelvin-Helmholtz instabilities. However, such shear instabilities are induced by the boundary-layer separation in large-scale, opposing flows. This links the global nature of thick shell convection with the entrainment process. We establish the quantitative dependence of the entrainment rate on grid resolution. With our numerical technique simulations with $1024^3$ cells or more are required to reach a numerical fidelity appropriate for this problem. However, only the result from the $1536^3$ simulation provides a clear indication that we approach convergence with regard to the entrainment rate. Our results demonstrate that our method, which is described in detail, can provide quantitative results related to entrainment and convective boundary mixing in deep stellar interior environments with veryvstiff convective boundaries. For the representative case we study in detail, we find an entrainment rate of $4.38 pm 1.48 times 10^{-13}M_odot mathrm{/s}$.
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The He-shell flash convection in AGB stars is the site for the high-temperature component of the s-process in low- and intermediate mass giants, driven by the Ne22 neutron source. [...] The upper convection boundary plays a critical role during the H-ingestion episode that may lead to neutron-bursts in the most metal-poor AGB stars. We address these problems through global 3-dimensional hydrodynamic simulations including the entire spherical He-shell flash convection zone (as oposed to the 3D box-in-a-star simulations). An important aspect of our current effort is to establish the feasibility of our appoach. We explain why we favour the explicit treatment over the anelastic approximation for this problem. The simulations presented in this paper use a Cartesian grid of 512^3 cells and have been run on four 8-core workstations for four days to simulate ~5000s, which corresponds to almost ten convective turn-over times. The convection layer extends radially at the simulated point in the flash evolution over 7 H_p pressure scale-heights and exceeds the size of the underlying core. Convection is dominated by large convective cells that fill more than an entire octant. [...]
Context. Multidimensional hydrodynamic simulations of convection in stellar interiors are numerically challenging, especially for flows at low Mach numbers. Methods. We explore the benefits of using a low-Mach hydrodynamic flux solver and demonstrate its usability for simulations in the astrophysical context. The time-implicit Seven-League Hydro (SLH) code was used to perform multidimensional simulations of convective helium shell burning based on a 25 M$_odot$ star model. The results obtained with the low-Mach AUSM$^{+}$-up solver were compared to results when using its non low-Mach variant AUSM$_mathrm{B}^{+}$-up. We applied well-balancing of the gravitational source term to maintain the initial hydrostatic background stratification. The computational grids have resolutions ranging from $180 times 90^2$ to $810 times 540^2$ cells and the nuclear energy release was boosted by factors of $3 times 10^3$, $1 times 10^4$, and $3 times 10^4$ to study the dependence of the results on these parameters. Results. The boosted energy input results in convection at Mach numbers in the range of $10^{-2}$ to $10^{-3}$. Standard mixing-length theory (MLT) predicts convective velocities of about $1.6 times 10^{-4}$ if no boosting is applied. 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$^{+}_{mathrm{B}}$ -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.
Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers as the Sun. As a function of the magnetic Reynolds number (${rm Rm}$), the growth rate of the dynamo is consistent with an ${rm Rm}^{1/2}$ scaling. No evidence for a logarithmic increase of the growth rate with ${rm Rm}$ is found.
We present a statistical analysis of turbulent convection in stars within our Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we derived from first principles. The primary results reported in this document include: (1) an extensive set of mean-field equations for compressible, multi-species hydrodynamics, and (2) corresponding mean-field data computed from various simulation models. Some supplementary scale analysis data is also presented. The simulation data which is presented includes: (1) shell convection during oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection in a 5 solar mass red giant, (3) shell convection during the helium flash, and (4) a hydrogen injection flash in a 1.25 solar mass star. These simulations have been partially described previously in Meakin [2006], Meakin and Arnett [2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and Mocak et al. [2009, 2011]. New data is also included in this document with several new domain and resolution configurations as well as some variations in the physical model such as convection zone depth and driving source term. The long term goal of this work is to aid in the development of more sophisticated models for treating hydrodynamic phenomena (e.g., turbulent convection) in the field of stellar evolution by providing a direct link between 3D simulation data and the mean fields which are modeled by 1D stellar evolution codes. As such, this data can be used to test previously proposed turbulence models found in the literature and sometimes used in stellar modeling. This data can also serve to test basic physical principles for model building and inspire new prescriptions for use in 1D evolution codes.
Convection is the mechanism by which energy is transported through the outermost 30% of the Sun. Solar turbulent convection is notoriously difficult to model across the entire convection zone where the density spans many orders of magnitude. In this issue of PNAS, Hanasoge et al. (2012) employ recent helioseismic observations to derive stringent empirical constraints on the amplitude of large-scale convective velocities in the solar interior. They report an upper limit that is far smaller than predicted by a popular hydrodynamic numerical simulation.
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