Two-dimensional models of fast rotating stars and mixing processes

In this short review we present the recent progresses in modelling fast rotating stars in two dimensions. We thus give a brief description of the features of the public domain code ESTER that can compute self-consistently the structure and the large-scale flows (differential rotation and meridional circulation) of an axisymmetric stellar model of a (fast) rotating early-type main sequence star. We illustrate these modelling with the recent results obtained on Altair, a nearby extremely fast rotator. We then discuss the various way mixing takes place in the stably stratified radiative envelope of early-type stars, and especially in massive ones where the radiative winds add a new source of large-scale flows, which are shown to be strongly anisotropic and very difficult to represent in one dimension.