Interest in 3-D radiative transfer in stellar atmospheres has grown with the calculations of Asplund and collaborators (Grevesse et al., 2007; Asplund, 2000; Asplund et al., 1999; Asplund et al., 2000; Asplund et al., 2005). This work has indicated that the solar oxygen abundance needs to be revised downward. However, the revised abundances are difficult to reconcile with helioseismological results (see Basu & Antia, 2008, and references therein). The work of Asplund et al. is based on comparisons of synthetic spectra produced by formal solutions of hydrodynamical models of solar convection. We present a framework for solving the full scattering problem that is applicable to hydrodynamical calculations of stellar atmospheres. Hauschildt & Baron (2006, hereafter: Paper I) and Baron & Hauschildt (2007, hereafter: Paper II) described a framework for the solution of the radiative transfer equation for scattering continua and lines in 3D (when we say 3D we mean three spatial dimensions, plus three momentum dimensions) for the time independent, static case. In the 3rd paper of this series we apply these methods to problems with period boundary conditions which typically arise in radiation-hydrodynamical simulations of convective atmospheres. In such calculations the radiation transport has to be simplified compared to the full problem in order to keep the calculations tractable. However, a full solution of the scattering line problem is needed for comparison and post-processing of the structures.

We describe our method, its rate of convergence, and present comparisons to our well-tested 1-D calculations.