Convection in giant stars

The observed brightness fluctuations and large-scale structures on the surface of the Red Supergiant Betelgeuse make the star a prime targed for future interferometric measurements. At the same time, they open the possibility to resolve these structures in numerical radiation hydrodynamics simulations of the entire star. After some general remarks about the possibility and difficulties of 3D simulations of stars in general results of such calcuations of the outer convective envelope and the atmosphere of a Red Supergiant and a star on the Asmyptotic Giant Branch are presented. These show that numerous short-lived small-scale surface granules coexist with a few long-lived large-scale envelope convection cells. Pressure fluctuations deform the star and influence the surface convection. The convective "granulation" pattern differs from the solar one. Convection and pulsations produce large-scale high-contrast brightness fluctuations that might explain the observed luminosity variations and surface "spots". Shock waves and supersonic atmospheric velocities manifest themselves in broad line profiles.