  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 evolution 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.
