The observed brightness fluctuations and large-scale structures on thesurface of the Red Supergiant Betelgeuse make the star a prime targedfor future interferometric measurements. At the same time, they openthe possibility to resolve these structures in numerical radiationhydrodynamics simulations of the entire star. After some general remarksabout the possibility and difficulties of 3D simulations of stars ingeneral results of such calcuations of the outer convective envelope andthe atmosphere of a Red Supergiant and a star on the Asmyptotic GiantBranch are presented. These show that numerous short-lived small-scalesurface granules coexist with a few long-lived large-scale envelopeconvection cells. Pressure fluctuations deform the star and influencethe surface convection. The convective “granulation" pattern differsfrom the solar one. Convection and pulsations produce large-scalehigh-contrast brightness fluctuations that might explain the observedluminosity variations and surface “spots”. Shock waves and supersonicatmospheric velocities manifest themselves in broad line profiles.