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. [...]
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