The Discrete Ordinates Method (DOM) is the most widely used velocity discretization method for simulating the radiative transport equation. The ray effect stands as a long-standing drawback of DOM. In benchmark tests displaying the ray effect, we observe low regularity in velocity within the solution. To address this issue, we propose a random ordinate method (ROM) to mitigate the ray effect. Compared with other strategies proposed in the literature for mitigating the ray effect, ROM offers several advantages: 1) the computational cost is comparable to DOM; 2) it is simple and requires minimal changes to existing code based on DOM; 3) it is easily parallelizable and independent of the problem setup. Analytical results are presented for the convergence orders of the error and bias, and numerical tests demonstrate its effectiveness in mitigating the ray effect.

翻译：离散纵标法（DOM）是模拟辐射传输方程中最广泛使用的速度离散化方法。射线效应是DOM长期存在的缺陷。在展示射线效应的基准测试中，我们观察到解在速度维度上呈现低正则性。为解决此问题，本文提出一种随机离散纵标法（ROM）以缓解射线效应。与文献中提出的其他缓解射线效应策略相比，ROM具有以下优势：1) 计算成本与DOM相当；2) 方法简洁，对现有基于DOM的代码仅需最小改动；3) 易于并行化且独立于具体问题设置。本文给出了误差与偏差收敛阶的理论分析结果，并通过数值实验验证了该方法在缓解射线效应方面的有效性。