Ray Effect in Rarefied Flow Simulation

TL;DR

This paper investigates the ray effect in rarefied flow simulations using discrete velocity methods, analyzes its causes, impacts, and proposes strategies to minimize it, highlighting the advantages of particle methods in complex, non-equilibrium flows.

Contribution

It provides a detailed theoretical and numerical analysis of the ray effect in rarefied flow simulations and introduces an adaptive discretization strategy to mitigate it.

Findings

Ray effect significantly affects the accuracy of DVM in rarefied flows.

Optimal velocity discretization is problem-dependent and challenging to determine.

Particle methods inherently avoid the ray effect due to their self-adaptive nature.

Abstract

Ray effect usually appears in the radiative transfer when using discrete ordinates method (DOM) in the simulations. The cause and remedy for the ray effect have been intensively investigated in the radiation community. For rarefied gas flow, the ray effect is also associated with the discrete velocity method (DVM). However, few studies have been carried out in the rarefied community. In this paper, we take a detailed investigation of the ray effect in the rarefied flow simulations. Starting from a few commonly used benchmark tests, the root of the ray effect has been analyzed theoretically and validated numerically. At the same time, the influence of the ray effect on the quality of the numerical results of rarefied flow is estimated quantitatively. After understanding the nature of the ray effect, the strategy to minimize the ray effect through the discretization of the particle velocity space is presented and applied in the numerical simulations. An optimal velocity discretization for DVM is problem dependent and can be hardly obtained in the complex flow simulations. Due to the intrinsic self-adaptation of particle velocity, the stochastic particle methods are free from the ray effect. In rarefied regimes, the particle method seems more appropriate in the capturing of highly non-equilibrium flow behavior.