A numerical method successfully applied to several astrophysical problems is adapted for investigating the dynamical evolution of dust driven stellar winds in long period variables (LPVs). The model provides the solution of the full nonlinear system of radiation hydrodynamics together with a simple parameterized description of the dust formation. The numerical procedure is based on an adaptive grid which distributes the grid points at locations of large gradients. All equations are written in conservation form and a monotonic second order transport scheme is used to advect the physical variables through the cell boundaries.
The aim of this paper is to introduce this new method, compare it to existing models and to discuss in detail the differences arising from different physical input and the numerical method. In order to allow for qualitative and quantitative comparisons we present the results of first test calculations with parameters corresponding to the standard model of Bowen (1988).
A&A 273, 513
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