Radiative hydrodynamics models of stellar convection

In the quest for a better theoretical understanding of the dynamical processes operating in stellar envelopes, increasingly more realistic hydrodynamical models of stellar convection have been developed over the last 25 years. Based on 3D state-of-the-art simulations performed recently with the radiation hydrodynamics code CO⁵BOLD, we review the present status of hydrodynamical modeling of stellar surface convection and demonstrate the basic differences between 3D hydrodynamical models and 1D `classical' hydrostatic atmospheres where convection is treated by the mixing-length theory. We briefly discuss some of the many possible applications across the Hertzsprung-Russell diagram, including spectroscopic abundance determinations using 3D stellar atmospheres, particularly with regard to the much debated question of the solar oxygen abundance.