  Solving the radiation transport equation is a challenging task, due to the
high dimensionality of the solution's phase space. The commonly used discrete
ordinates (S$_N$) method suffers from ray effects which result from a break in
rotational symmetry from the finite set of directions chosen by S$_N$. The
spherical harmonics (P$_N$) equations, on the other hand, preserve rotational
symmetry, but can produce negative particle densities. The discrete ordinates
(S$_N$) method, in turn, by construction ensures non-negative particle
densities.
  In this paper we present a modified version of the S$_N$ method, the rotated
S$_N$ (rS$_N$) method. Compared to S$_N$, we add a rotation and interpolation
step for the angular quadrature points and the respective function values after
every time step. Thereby, the number of directions on which the solution
evolves is effectively increased and ray effects are mitigated. Solution values
on rotated ordinates are computed by an interpolation step. Implementation
details are provided and in our experiments the rotation/interpolation step
only adds 5% to 10% to the runtime of the S$_N$ method. We apply the rS$_N$
method to the line-source and a lattice test case, both being prone to
ray-effects. Ray effects are reduced significantly, even for small numbers of
quadrature points. The rS$_N$ method yields qualitatively similar solutions to
the S$_N$ method with less than a third of the number of quadrature points,
both for the line-source and the lattice problem. The code used to produce our
results is freely available and can be downloaded.
