  Aims. We present the implementation of the treatment of particle ejection and
dust nucleation in the smoothed particle hydrodynamics (SPH) code phantom.
These developments represent the first step toward a more complete modeling of
dust-driven winds emanating from AGB stars. Methods. The AGB outflow is modeled
by injecting the SPH particles from a spherical inner boundary. This boundary
is a series of concentric shells, with the AGB star at its center, and the
particles are positioned on these shells on the vertices of an isocahedron
geodesic surface. The outermost shell is ejected with a predefined radial
velocity, and subsequent lower shells replenish the ejected ones, all rotated
randomly to improve the isotropy of the outflow. The physical properties of the
particles on these shells are set by solving the 1D analytic steady wind
equations. The formation of dust is calculated starting from a compact chemical
network for carbon-rich material, which creates the building blocks of the
solid-state particles. Subsequently, the theory of the moments is used to
obtain dust growth rates, without requiring knowledge on the grain size
distribution. Results. We tested our implementation against a series of 1D
reference solutions. We demonstrate that our method is able to reproduce
Parker-type wind solutions. For the trans-sonic solution, small oscillations
are present in the vicinity of the sonic point, but these do not impact the
trans-sonic passage or terminal wind velocity. Supersonic solutions always
compare nicely with 1D analytic profiles. We also tested our implementation of
dust using two formalisms: an analytic prescription for the opacity devised by
Bowen and the full treatment of carbon-dust formation. Both simulations
reproduce the 1D analytic solution displaying the expected additional
acceleration when the gas temperature falls below the condensation temperature.
