  Solving the radiative transfer equation with the discrete ordinates (S$_N$)
method leads to a non-physical imprint of the chosen quadrature set on the
solution. To mitigate these so-called ray effects, we propose a modification of
the S$_N$ method, which we call artificial scattering S$_N$ (as-S$_N$). The
method adds an artificial forward-peaked scattering operator which generates
angular diffusion to the solution and thereby mitigates ray effects. Similar to
artificial viscosity for spatial discretizations, the additional term vanishes
as the number of ordinates approaches infinity. Our method allows an efficient
implementation of explicit and implicit time integration according to standard
S$_N$ solver technology. For two test cases, we demonstrate a significant
reduction of the error for the as-S$_N$ method when compared to the standard
S$_N$ method, both for explicit and implicit computations. Furthermore, we show
that a prescribed numerical precision can be reached with less memory due to
the reduction in the number of ordinates.
