Numerical simulations of stellar winds: polytropic models

We discuss steady-state transonic outflows obtained by direct numerical sol ution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (h yperbolic) partial differential equations. We proceed stepwise from a spher ically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arr ive at axisymmetric, polytropic, magnetized, rotating models. These represe nt 2D generalisations of the analytical ID Weber-Davis wind solution, which we obtain in the process. Axisymmetric wind solutions containing both a 'w ind' and a 'dead' zone are presented. Since we are solving for steady-state solutions, we efficiently exploit ful ly implicit time stepping. The method allows us to model thermally and/or m agneto-centrifugally driven stellar outflows. We particularly emphasize the boundary conditions imposed at the stellar surface. For these axisymmetric , steady-state solutions, we can use the knowledge of the flux functions to verify the physical correctness of the numerical solutions.