The Discrete Ordinates Method (DOM) is the most widely used velocity discretization method for simulating the radiative transport equation. However, the ray effect is a long-standing drawback of DOM. In benchmark tests that exhibit the ray effect, we observe low regularity in the velocity variable of the solution. To address this issue, we propose a Random Ordinate Method (ROM) to mitigate the ray effect. Compared to other strategies proposed in the literature for mitigating the ray effect, ROM offers several advantages: 1) For benchmark tests that exhibit ray effect, the computational cost is lower than that of the DOM; 2) it is simple and requires minimal changes to existing DOM-based code; 3) it is easily parallelizable and independent of the problem setup. A formal analysis is presented for the convergence orders of the error and bias. Numerical tests demonstrate the reduction in computational cost compared to DOM, as well as its effectiveness in mitigating the ray effect.

翻译：离散坐标法（DOM）是模拟辐射输运方程最广泛使用的速度离散化方法。然而，射线效应是DOM长期存在的一个缺点。在呈现射线效应的基准测试中，我们观察到解在速度变量上具有低正则性。为解决此问题，我们提出了一种随机坐标法（ROM）来缓解射线效应。与文献中提出的其他缓解射线效应的策略相比，ROM具有以下几个优点：1) 对于呈现射线效应的基准测试，其计算成本低于DOM；2) 方法简单，对现有基于DOM的代码只需极少的改动；3) 易于并行化，且独立于问题设置。本文对误差和偏差的收敛阶进行了形式化分析。数值测试证明了与DOM相比计算成本的降低，以及其在缓解射线效应方面的有效性。