Dynamic model atmospheres of cool giants

Cool giant stars are highly dynamical objects, and complex micro-physical processes play an important role in their extended atmospheres and winds. The interpretation of observations, and in particular of high-resolution IR spectra, requires realistic self-consistent model atmospheres. Current dynamical models include rather detailed micro-physics, and the resulting synthetic spectra compare reasonably well with observations. A transition from qualitative to quantitative modelling is taking place at present. We give an overview of existing dynamical model atmospheres for AGB stars, discussing recent advances and current trends in modelling, including 3D 'star-in-a-box' models. When comparing synthetic spectra and other observable properties resulting from dynamical models with observations we focus on the near- and mid-IR wavelength range.