  Stellar winds observed in asymptotic giant branch (AGB) stars are usually
attributed to a combination of stellar pulsations and radiation pressure on
dust. Shock waves triggered by pulsations propagate through the atmosphere,
compressing the gas and lifting it to cooler regions, which create favourable
conditions for grain growth. If sufficient radiative acceleration is exerted on
the newly formed grains through absorption or scattering of stellar photons, an
outflow can be triggered. Strong candidates for wind-driving dust species in
M-type AGB stars are magnesium silicates (Mg$_2$SiO$_4$ and MgSiO$_3$). Such
grains can form close to the stellar surface, they consist of abundant
materials and, if they grow to sizes comparable to the wavelength of the
stellar flux maximum, they experience strong acceleration by photon scattering.
  We use a frequency-dependent radiation-hydrodynamics code with a detailed
description for the growth of Mg$_2$SiO$_4$ grains to calculate the first
extensive set of time-dependent wind models for M-type AGB stars. The resulting
wind properties, visual and near-IR photometry and mid-IR spectra are compared
with observations.We show that the models can produce outflows for a wide range
of stellar parameters. We also demonstrate that they reproduce observed
mass-loss rates and wind velocities, as well as visual and near-IR photometry.
However, the current models do not show the characteristic silicate features at
10 and 18 $\mu$m as a result of the cool temperature of Mg$_2$SiO$_4$ grains in
the wind. Including a small amount of Fe in the grains further out in the
circumstellar envelope will increase the grain temperature and result in
pronounced silicate features, without significantly affecting the photometry in
the visual and near-IR wavelength regions.
