  The purpose of this work is to present an extensive grid of dynamical
atmosphere and wind models for M-type AGB stars, covering a wide range of
relevant stellar parameters. We used the DARWIN code, which includes
frequency-dependent radiation-hydrodynamics and a time-dependent description of
dust condensation and evaporation, to simulate the dynamical atmosphere. The
wind-driving mechanism is photon scattering on submicron-sized Mg$_2$SiO$_4$
grains. The grid consists of $\sim4000$ models, with luminosities from
$L_\star=890\,{\mathrm{L}}_\odot$ to $L_\star=40000\,{\mathrm{L}}_\odot$ and
effective temperatures from 2200K to 3400K. For the first time different
current stellar masses are explored with M-type DARWIN models, ranging from
0.75M$_\odot$ to 3M$_\odot$. The modelling results are radial atmospheric
structures, dynamical properties such as mass-loss rates and wind velocities,
and dust properties (e.g. grain sizes, dust-to-gas ratios, and degree of
condensed Si). We find that the mass-loss rates of the models correlate
strongly with luminosity. They also correlate with the ratio $L_*/M_*$:
increasing $L_*/M_*$ by an order of magnitude increases the mass-loss rates by
about three orders of magnitude, which may naturally create a superwind regime
in evolution models. There is, however, no discernible trend of mass-loss rate
with effective temperature, in contrast to what is found for C-type AGB stars.
We also find that the mass-loss rates level off at luminosities higher than
$\sim14000\,{\mathrm{L}}_\odot$, and consequently at pulsation periods longer
than $\sim800$ days. The final grain radii range from 0.25 micron to 0.6
micron. The amount of condensed Si is typically between 10% and 40%, with
gas-to-dust mass ratios between 500 and 4000.
