Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering

TL;DR

This paper introduces the artificial scattering S$_N$ (as-S$_N$) method, which mitigates ray effects in the discrete ordinates approach for radiative transfer by adding an artificial scattering term, improving accuracy and efficiency.

Contribution

The paper proposes a novel modification to the S$_N$ method, called as-S$_N$, that reduces ray effects through artificial scattering, with demonstrated improvements in accuracy and memory efficiency.

Findings

Significant error reduction in test cases with as-S$_N$ compared to standard S$_N$.

Effective mitigation of ray effects using artificial scattering.

Reduced memory requirements due to fewer ordinates needed.

Abstract

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.