Cool atmospheres from low-mass stars over brown dwarfs to gas giant planets, hot Neptunes and super-Earths show atmospheric dynamic driven by convective instability and global energy transport. Classical 1D and local 2D and 3D simulations allow, within parameterised approaches like mixing length theory, and radiative hydrodynamics (RHD) the modelling of convective velocity fields, overshoot and phenomena like gravity waves. This description of atmospheric dynamics has been successfully applied in physically detailed 1D models to quantitatively describe molecular advection and condensate formation, reproducing the various cloud formation patterns and non-equilibrium chemistry observed with decreasing temperature in substellar atmospheres.

To take into account rotation effects, irradiation in close-in planets and time evolution of atmospheric features however global models are required, where general circulatation models (GSMs) have allowed to estimate the effect of the associated large-scale circulation patterns on local dynamics. But a new generation of global RHD models mapping the vertically and horizontally fully resolved convective structure onto a downscaled model of the entire star, brown dwarf or planet. These models allow us to study convectively driven large-scale structures that may explain the observed variability in many brown dwarfs, and form a new tool for understanding rotating and irradiated planets.