  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.
