## 2. Time-dependent numerical hydrodynamicsWe have applied two different computer codes to study the time-dependent hydrodynamics of circumstellar gas/dust shells. In the following we briefly describe their main features. ## 2.1. DEXCEL: two-component radiation hydrodynamics
This two-component (gas / dust) radiation hydrodynamics code is
designed to model a stellar wind driven by radiation pressure on dust
grains and subsequent momentum transfer to the gas component via
dust-gas collisions. The coupled equations of hydrodynamics and
frequency-dependent radiative transfer governing the structure and
temporal evolution of circumstellar gas/dust shells are solved
numerically, with a The numerical scheme adopted here for the solution of the system of
the Eulerian hydrodynamics / radiative transfer equations in spherical
geometry is fully implicit. Hence, the time step of the simulations is
All DEXCEL models used for this investigation have radial grid points spaced according to In order to fully resolve the dust acceleration region, the
parameter Further details of the underlying physical assumptions and the numerical procedure being employed have been given by Steffen et al. (1998, henceforth SSS98). We point out that this code was not designed for a detailed
modeling of the thermal structure of the ## 2.2. NEBEL: one-component, Godunov-type hydrodynamicsThe one-component, explicit code NEBEL solves the Eulerian equations of hydrodynamics in spherical geometry together with the rate equations describing time-dependent ionization / recombination of astrophysical plasmas. The numerical scheme is based on a high-resolution second-order Godunov-type advection scheme ("wave propagation method", Le Veque 1997), including an approximate Riemann solver. This inherently conservative method adequately calculates the propagation and interaction of non-linear waves at each cell boundary. It is therefore particularly well suited to resolve even strong shocks, which can arise, e.g. due to interacting winds. The equation of state is that of an ideal gas of solar composition (including partial ionization). For more details about the NEBEL code, which was actually designed to compute the evolution of planetary nebulae, see Kifonidis (1996), Perinotto et al. (1998) and Kifonidis et al. (2000). Note that in contrast to the two-component radiation hydrodynamics
code described above, this code does where is the cooling rate per
unit mass in erg/g/s. This function was constructed from the cooling
rate for H Since the NEBEL code does not account for radiation pressure and gravity, it has been applied only to regions of the wind where these external forces are negligible in comparison to the internal forces (thermal pressure, viscosity). From steady-state models of dust-driven AGB winds obtained with DEXCEL (Steffen et al. 1997), we find that for the parameters considered in the following the acceleration region is restricted to the inner parts of the outflow, cm. In order to recompute a given problem with NEBEL, we use the values of gas velocity, density, and temperature at cm, , computed before by DEXCEL as a time-dependent inner boundary condition for the NEBEL code. In this way, the results of the two codes may be compared in the outer wind region ( cm). It is impossible, however, to study the acceleration region ( cm) with NEBEL. All NEBEL models used for this investigation have
radial grid points, also spaced
according to Eq. (1). The parameter © European Southern Observatory (ESO) 2000 Online publication: May 3, 2000 |