Published online by Cambridge University Press: 12 April 2016
We have obtained detailed 2-dimensional models of the surface layers of solar-type stars from extensive numerical simulations solving the time-dependent, non-linear equations of hydrodynamics for a stratified compressible fluid. The calculations take into account a realistic equation of state (including ionization of H and He as well as formation of H2-molecules) and use an elaborate scheme to describe multi-dimensional, non-local, frequency-dependent radiative transfer. The hydrodynamical models include the photosphere as well as part of the convective subphotospheric layers, with an open lower boundary located about one pressure scale height (~ 320 km) below TRoss = 1, allowing a free flow of gas out of and into the model. A fixed specific entropy, s*, is (asymptotically) assigned to the gas entering the simulation volume from below, which uniquely determines the effective temperature of the hydrodynamical model. For details about the physical assumptions, numerical method and characteristics of the resulting convective flow at the solar surface see Steffen (1991); Steffen and Freytag (1991).