The cool extended atmospheres of late type giants are sites where dust formation takes place. Radiation pressure on the dust grains is an important force for driving the slow but massive winds observed in such objects. Existing calculations of dust driven stellar winds (e.g. Bowen 1988, Fleischer et al. 1991) suffer from the fact that they include approximations at various levels for different parts of the problem like the hydrodynamics or the dust formation. Furthermore they do not include time-dependent radiative transfer.

In order to overcome these insufficiencies we plan to calculate self-consistent models of dust driven winds with a full description of both the radiation hydrodynamics and the time-dependent dust formation. As a first step, however, we concentrate our investigations on the self-consistent description of the radiation hydrodynamics adopting only a simple description of the dust opacities.