  3-D astrophysical atmospheres will have random velocity fields. We seek to
combine the methods we have developed for solving the 1-D problem with
arbitrary flows to those that we have developed for solving the fully 3-D
relativistic radiative transfer problem in the case of monotonic flows. The
methods developed in the case of 3-D 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
3-D. Simultaneously, the techniques we developed for treating the 1-D problem
with arbitrary velocity fields are easily adapted to the 3-D problem. The
algorithm we present allows the solution of 3-D 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.
