Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering
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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.
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