SIMBAD references

General 3D astrophysical atmospheres will have random velocity fields. We seek to combine the methods we have developed for solving the 1D problem with arbitrary flows to those that we have developed for solving the fully 3D relativistic radiative transfer problem for monotonic flows. The methods developed for 3D atmospheres with monotonic flows, solving the fully relativistic problem along curves defined by an affine parameter, are very flexible and can be extended to the case of arbitrary velocity fields in 3D. Simultaneously, the techniques we developed for treating the 1D problem with arbitrary velocity fields are easily adapted to the 3D problem. The algorithm we present can be used to solve 3D radiative transfer problems that include arbitrary wavelength couplings. We use a quasi-analytic formal solution of the radiative transfer equation that significantly improves the overall computation speed. We show that the approximate lambda operator developed in previous work gives good convergence, even neglecting wavelength coupling. Ng acceleration also gives good results. We present tests that are of similar resolution to what has been presented using Monte-Carlo techniques, thus our methods will be applicable to problems outside of our test setup. Additional domain decomposition parallelization strategies will be explored in future work.