Solar and stellar coronal models driven with Alfvén and kink waves

In recent years, the so-called AWSOM models are a new generation of solar and stellar atmospheric models, which incorporate the heating and forces of Alfv\'en waves on top of more classical effects. They are capturing well the stellar coronae, but from comparison with solar observations, we know that they lack heating in polar open field regions.
In this contribution, I will describe our theoretical development of a new formalism that allows to describe the kink waves associated with density structures in stellar coronae. I will explain the governing equations, and how the kink waves can provide extra heating power in the open field regions, that more adequately describe the heating and driving of the stellar wind. The system of equations have now been implemented in 3D numerical codes. I will use such simulations to show that kink wave heating outperforms the heating by Alfven waves. I will show how the new simulation tools may be used to construct 3D models of coronae of cool stars.