  Models describing dust-driven winds are important for understanding the
physical mechanism and properties of mass loss on the asymptotic giant branch.
These models are becoming increasingly realistic with more detailed physics
included, but also more computationally demanding. The purpose of this study is
to clarify to what extent the applied numerical approach affects resulting
physical structures of modelled winds, and to discuss resulting changes.
Following the previously developed radiation hydrodynamic model - which
includes descriptions for time-dependent dust formation and gas-dust drift -
and using its physical assumptions and parameters, numerical improvements are
introduced. Impacts of the so-called adaptive grid equation and advection
schemes are assessed from models calculated with different numerical setups.
Results show that wind models are strongly influenced by numerical imprecision,
displaying differences in calculated physical properties of up to one hundred
per cent. Using a non-adaptive grid, models become periodic (in multiples of
stellar pulsation periods), instead of irregular, as obtained previously.
Furthermore, the numerical improvements reveal changes in physical structures.
The influence of gas-dust drift is confirmed to be highly important, in
particular for the dust component. Gas and dust are less tightly coupled than
previously, and drastically larger amounts of dust form assuming drift.
