AbstractLocal three-dimensional radiation-hydrodynamics simulations of patches of the surfaces of solar-type stars, that are governed by small-scale granular convection, have helped analyzing and interpreting observations for decades. These models contributed considerably to the understanding of the atmospheres and indirectly also of the interiors and the active layers above the surface of these stars. Of great help was of course the availability of a close-by prototype of these stars – the sun.In the case of an asymptotic-giant-branch (AGB) star, the convective cells have sizes comparable to the radius of the giant. Therefore, the extensions of the solar-type-star simulations to AGB stars have to be global and cover the entire object, including a large part of the convection zone, the molecule-formation layers in the inner atmosphere, and the dust-formation region in the outer atmosphere. Three-dimensional radiation-hydrodynamics simulations with CO5BOLD show how the interplay of large and small convection cells, waves, pulsations, and shocks, but also molecular and dust opacities of AGB stars create conditions very different from those in the solar atmosphere.Recent CO5BOLD models account for frequency-dependent radiation transport and the formation of two independent dust species for an oxygen-rich composition. The drop of the comparably smooth temperature distribution below a threshold determines to onset of dust formation, further in, at higher temperatures, for aluminium oxides (Al2O3) than for silicates (Mg2SiO4). An uneven dust distribution is mostly caused by inhomogeneities in the density of the shocked gas.
THREE-DIMENSIONAL RADIATION-HYDRODYNAMICS CALCULATIONS OF THE ENVELOPES OF YOUNG PLANETS EMBEDDED IN PROTOPLANETARY DISKS