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. [...]
The evolution of the first generations of stars at zero or extremly low metallicity, and especially some crucial properties like the primary N14 production, is charactarized by convective-reactive mixing events that are mostly absent from similar evo
lution phases at solar-like metallicity. These episodes occur when unprocessed H-rich material is mixed accross a convective boundary into C12 rich He-burning material, as for example in He-shell flashes of extremely-low metallicity AGB stars. In this paper we describe the astrophysical context of such convective-reactive events, including the difficulty of current one-dimensional stellar evolution models to correctly simulate these evolutionary phases. We then describe the requirements and current state of modeling convective-reactive processes in the first stars environment. We demonstrate some of the new concepts that we are applying to this problem, i.e. the highly accurate PPB advection scheme in the framework of PPM hydrodynamic simulations of mixing accross a very stiff convective boundary. We show initial results of such simulations that address the first non-reactive step of this problem, which is the entrainment of H at the top boundary of the He-shell flash convection zone.
