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.

中文翻译：

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使用人工散射的离散纵坐标法的射线效应减轻

使用离散纵坐标 (S$_N$) 方法求解辐射传递方程会在解上产生所选正交集的非物理印记。为了减轻这些所谓的射线效应，我们建议修改 S$_N$ 方法，我们将其称为人工散射 S$_N$ (as-S$_N$)。该方法添加了一个人工前向峰值散射算子，该算子对解产生角扩散，从而减轻射线效应。类似于空间离散化的人工粘性，附加项随着坐标数接近无穷大而消失。我们的方法允许根据标准 S$_N$ 求解器技术有效实现显式和隐式时间积分。对于两个测试用例，与标准 S$_N$ 方法相比，我们证明了 as-S$_N$ 方法的误差显着减少，无论是显式还是隐式计算。此外，我们表明，由于纵坐标数量的减少，可以以更少的内存达到规定的数值精度。