Random ordinate method for mitigating the ray effect in radiative transport equation simulations

TL;DR

This paper introduces a Random Ordinate Method (ROM) that effectively reduces the ray effect in radiative transport simulations, offering lower computational costs and easier implementation compared to traditional methods.

Contribution

The paper proposes a novel Random Ordinate Method (ROM) that mitigates the ray effect in the discrete ordinates method with lower cost and simpler integration.

Findings

ROM reduces ray effect in benchmark tests

ROM has lower computational cost than DOM

Numerical results confirm effectiveness of ROM

Abstract

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.