  Radiative acceleration of newly-formed dust grains and transfer of momentum
from the dust to the gas plays an important role for driving winds of AGB
stars. Therefore a detailed description of the interaction of gas and dust is a
prerequisite for realistic models of such winds. In this paper we present the
method and first results of a three-component time-dependent model of
dust-driven AGB star winds. With the model we plan to study the role and
effects of the gas-dust interaction on the mass loss and wind formation. The
wind model includes separate conservation laws for each of the three components
of gas, dust and the radiation field and is developed from an existing model
which assumes position coupling between the gas and the dust. As a new feature
we introduce a separate equation of motion for the dust component in order to
fully separate the dust phase from the gas phase. The transfer of mass, energy
and momentum between the phases is treated by interaction terms. We also carry
out a detailed study of the physical form and influence of the momentum
transfer term (the drag force) and three approximations to it. In the present
study we are interested mainly in the effect of the new treatment of the dust
velocity on dust-induced instabilities in the wind. As we want to study the
consequences of the additional freedom of the dust velocity on the model we
calculate winds both with and without the separate dust equation of motion. The
wind models are calculated for several sets of stellar parameters. We find that
there is a higher threshold in the carbon/oxygen abundance ratio at which winds
form in the new model. The winds of the new models, which include drift, differ
from the previously stationary winds, and the winds with the lowest mass loss
rates no longer form.
