Evaluation of Ray Effects in Linear Transport Problems

Abstract

The adoption of a angular discretization scheme in the solution of the linear transport equation is introducing a wide range of distortions associated with the propagation of particles along discrete directions, usually called ray effects. These numerical artifacts and the consequent distortion of the physical description are observed in multidimensional configurations in steady-state and also in the one-dimensional case when the time-dependence is considered. Through the analysis of simplified configurations, this work aims at a characterization of the ray effect phenomenon. Steady-state and time-dependent problems are solved analytically and then compared to the results obtained by applying discrete ordinates, clearly isolating ray effects from other numerical effects and allowing the quantification of the physical distortion. The analysis of the transport kernel in the Fourier-transformed space permits the identification of a proper integral parameter, called ray effect indicator, to measure the distortion introduced in the transport model by the angular discretization. The efficiency of alternative schemes to the standard S_N approach for the reduction of ray effects is also discussed.

Keywords:

• linear transport
• time-ray effects
• angular discretization schemes
• Fourier transform