Dust formation in winds of long-period variables. I - Equations, method of solution, simple examples

Time-dependent numerical calculations of the formation and growth of dust particles in stellar winds are presented. The production rate and the properties of the dust are obtained by solving the moment equations derived by Gail & Sedlmayr (1988) and generalized by Gauger et al. (1990). The equations are reformulated to allow arbitrary motions of grid points. The numerical technique used is similar to an implicit formulation of the equations of radiation hydrodynamics in conservative form and will allow an incorporation into the existing radiation hydrodynamics code. A new numerical method is calculated for the formation of carbon dust in stationary stellar winds around cool C-rich stars to compare these results with models available in the literature.