## 2. Modelling method and parametersWe solve the coupled system of radiation hydrodynamics and
time-dependent dust formation (cf. Höfner et al. 1995)
employing an implicit numerical method and an adaptive grid (for
details of the numerical technique see Dorfi & Feuchtinger 1995).
The gas dynamics including self-gravity is described by the equations
of continuity, motion and energy, and the radiation field by the grey
moment equations of the radiative transfer equation. The energy
exchange between matter and radiation adopts a LTE source function
which could result in overestimating the cooling rates behind
radiative shocks. Considering C-rich stars we assume the formation of
amorphous carbon grains. The extinction efficiency of the grains
( ; The pulsation of the long-period variable (LPV) is simulated by a sinusoidal motion of the inner boundary which is located below the stellar photosphere (). Since the radiative flux is kept constant at this point the luminosity at the inner boundary varies according to . The models are characterized by the following set of parameters:
stellar mass , luminosity ,
effective temperature and the carbon-to-oxygen
abundance ratio (all abundances except carbon
are assumed as solar) of the hydrostatic initial model as well as the
piston parameters period © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |