  Context: Observations of asymptotic giant branch (AGB) stars with increasing
spatial resolution reveal new layers of complexity of atmospheric processes on
a variety of scales. Aim: To analyze the physical mechanisms that cause
asymmetries and surface structures in observed images, we use detailed 3D
dynamical simulations of AGB stars; these simulations self-consistently
describe convection and pulsations. Methods: We used the CO5BOLD
radiation-hydrodynamics code to produce an exploratory grid of global
"star-in-a-box" models of the outer convective envelope and the inner
atmosphere of AGB stars to study convection, pulsations, and shock waves and
their dependence on stellar and numerical parameters. Results: The model
dynamics are governed by the interaction of long-lasting giant convection
cells, short-lived surface granules, and strong, radial, fundamental-mode
pulsations. Radial pulsations and shorter wavelength, traveling, acoustic waves
induce shocks on various scales in the atmosphere. Convection, waves, and
shocks all contribute to the dynamical pressure and, thus, to an increase of
the stellar radius and to a levitation of material into layers where dust can
form. Consequently, the resulting relation of pulsation period and stellar
radius is shifted toward larger radii compared to that of non-linear 1D models.
The dependence of pulsation period on luminosity agrees well with observed
relations. The interaction of the pulsation mode with the non-stationary
convective flow causes occasional amplitude changes and phase shifts. The
regularity of the pulsations decreases with decreasing gravity as the relative
size of convection cells increases. The model stars do not have a well-defined
surface. Instead, the light is emitted from a very extended inhomogeneous
atmosphere with a complex dynamic pattern of high-contrast features.
