Stars that start their lives with about 1-8 solar masses develop into luminous cool giants towards the end of their evolution (so-called AGB stars). These objects are strongly affected by dynamical processes. Giant convection cells reach deeply into the stellar interior and bring newly produced elements such as carbon to the surface. Stellar winds (i.e. outflows of matter from the stellar surface) lead to a runaway mass loss process, which eventually turns these stars into white dwarfs of typically 0.5-0.6 solar masses and enriches the surrounding interstellar medium with newly produced chemical elements. Radiative acceleration of dust grains is assumed to be the major source of momentum, driving the slow but dense outflows. Dust particles, which are formed in the cool outer layers of the atmosphere, are accelerated away from the star due to their interaction with stellar photons, and momentum is transferred to the surrounding gas by gas–grain collisions. Atmospheric shock waves, induced by stellar pulsations or convective motions, contribute significantly to this process by intermittently creating cool, dense layers of gas well above the photosphere where dust grains can form and grow efficiently. Detailed quantitative models of the dynamic atmospheres and winds are required to predict reliable mass loss rates, dust production rates and consistent synthetic spectra, which are necessary for understanding the evolution of stars and galaxies, and the cosmic origin of chemical elements. The applicants have substantial track records in developing internationally leading numerical models of stellar interiors, atmospheres and winds, as well as in combining theoretical results with state-of-the art observations. For comparisons to real stars, our models are sought after by observers, e.g. at front-line VLBI (Very Long Baseline Interferometry) instruments at ESO (European Southern Observatory) such as GRAVITY and more recently, MATISSE, ERIS. We have an ongoing collaboration with Markus Wittkowski at ESO Garching, Claudia Paladini at ESO Chile, and Josef Hron at Vienna university, that focuses on the interpretation of spatially resolved interferometric observations of AGB stars and red supergiants. The purpose of this NAISS application is to obtain the necessary computational resources for our most ambitious modelling projects, supported by a Swedish VR grant as well as a European ERC Advanced Grant (EXWINGS), and recently a KAW Scholar grant. The project includes two ongoing PhD projects. See also the Activity Report for NAISS 2023/5-138 for more details.