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.
