Tests with 3D structures

For a test with a computed 3D structure, we obtained an example snapshot structure from H-G. Ludwig (Wedemeyer et al., 2004; Caffau et al., 2007) of a radiation-hydrodynamical simulation of convection in the solar atmosphere. The radiation transport calculations were performed with a total of $141\times 141 \times 151$ grid points in $x$,$y$, and $z$, respectively, for a total of $3\,002\,031$ voxels, the periodic boundary conditions were set in the (horizontal) $x,y$ plane. The transport equation is solved for $n_\theta=16$ and $n_\phi=32$ solid angle points, so that a total of about $1.5\times 10^{9}$ intensities are calculated for each iteration and wavelength point. For the tests described here, we are only using the temperature-density structure of the hydro model and ignore the velocity field for the simple tests presented here. We set the continuum opacity proportional to the density $\rho$ by choosing a rough temperature independent estimate for the Rosseland mean opacity per unit mass of $0.1\,$cm$^2$/g and parameterizing the line in the same form as discussed above and in Paper II with a line total (wavelength integrated) opacity of $100$ times the local continuum and 32 wavelength points distributed over the full line profile.