Project summary

In this paper Woodward, Herwig & Lin demonstrate the PPMstar capabiltiy to construct converged entrainment simulations at the extremely stiff upper convective boundary when H-rich material may be ingested. This situation occurs in very-late thermal pulse post-AGB stars and in low-Z AGB stars. As an important result we provide evidence that full 4Pi geometry and 3-D simulations are required for H-ingestion simulations, and we provide a quantitative entrainment rate from our simulations. The numerical method is described in detail

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 (Sakurai's 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.  These very large-scale motions have
significant impact upon the flow behavior where the H-rich fluid is
entrained.  Additionally, we establish the quantitative dependence of
the entrainment rate on grid resolution. With our numerical technique
and with the relatively stiff convective boundaries that we find to
apply for H-entrainment into He-shell flash convection zones,
simulations with 1024^3 cells or more are required to reach a
numerical fidelity appropriate for the problem. However, only the
result from the 1536^3 simulation provides evidence that we do
reach 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 very stiff
convective boundaries. For the representative case we study in detail,
we find an entrainment rate of 4.38 +- 1.48 E-13Msun/s.