Signatures of convection in the atmospheres of cool evolved stars

Evolved cool stars of various masses are major cosmic engines, delivering substantial mechanical and radiative feedback to the interstellar medium through strong stellar winds and supernova ejecta. These stars play a pivotal role in enriching the interstellar medium with vital chemical elements that constitute the essential building blocks for the formation of subsequent generations of stars, planets, and potentially even life. Within the complex tapestry of processes occurring in the atmospheres of these cool and luminous stars, convection takes center stage. Convection is a non-local, complex phenomenon marked by non-linear interactions across diverse length scales within a multi-dimensional framework. For these particular stars, characterized by their considerable luminosities and extensive scale heights, convection transitions to a global scale. This transition is facilitated by the transmission of radiative energy through the non-uniform outer layers of their atmospheres. To have a full understanding of this phenomenon, the application of global comprehensive 3D radiation-hydrodynamics simulations of stellar convection is of paramount importance. We present two state-of-the-art numerical codes: CO5BOLD and Athena++. Furthermore, we provide a view on their applications as: pivotal roles in enabling a comprehensive investigation into the dynamic processes linked to convection; and critical tools for accurately modeling the emissions produced during shock breakouts in Type II-P supernovae.