Ray effect in rarefied flow simulation

Ray effect usually appears in the computation of radiative transfer when discrete ordinates method (DOM) is used. 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 make a detailed investigation of the ray effect in the rarefied flow simulation. Starting from a few commonly used benchmark tests, the root of the ray effect will be analyzed theoretically and validated numerically. The mitigation strategy by adjusting the discretization in the particle velocity space is studied as well. The guidelines are proposed to optimize the velocity space discretization for effectively reducing the ray effect. However, the design of optimal velocity space discretization is problem dependent and it can be hardly obtained in a highly rarefied flow simulation with complicated geometry. Due to the intrinsic self-adaptation of particle velocity, the stochastic particle method could automatically provide an optimized velocity discretization and avoid the ray effect. In the term of ray effect mitigation, the use of stochastic particle method is recommended in the numerical simulation of highly rarefied flow.