Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering

Solving the radiative transfer equation with the discrete ordinates (S) method leads to a nonphysical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S method that we call artificial scattering S (as-S). The method adds an artificial forward-peaked scattering operator that 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 solver technology. For two test cases, we demonstrate a significant reduction of error for the as-S method when compared to the standard S 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.