Radiative hydrodynamics in the highly super adiabatic layer of stellar   evolution models
  We present results of three dimensional simulations of the uppermost part of the sun, at 3 stages of its evolution. Each model includes physically realistic radiative-hydrodynamics (the Eddington approximation is used in the optically thin region), varying opacities and a realistic equation of state (full treatment of the ionization of H and He). In each evolution model, we investigate a domain, which starts at the top of the photosphere and ends just inside the convection zone (about 2400 km in the sun model). This includes all of the super-adiabatic layer (SAL). Due to the different positions of the three models in the $log (g) $ vs $log T_{eff}$ plane, the more evolved models have lower density atmospheres. The reduction in density causes the amount of overshoot into the radiation layer, to be greater in the more evolved models. 
F.J.Robinson, P.Demarque, S.Sofia (Yale University), K.L.Chan (Hong   Kong University of Science & Technology), Y.-C.Kim (Yo...