Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method

Abstract

The discrete ordinates method for the solution of the radiative heat transfer equation suffers from two main shortcomings, namely ray effects and numerical smearing. Spatial discretization, which is the cause of numerical smearing, constitutes the subject of the present work. Bounded skew high-order resolution schemes are applied to the discrete ordinate equations and compared with standard bounded high-order resolution schemes (CLAM, MUSCL, and SMART), as well as with the step scheme. Calculations are performed for two- and three-dimensional enclosures with transparent, emitting–absorbing, and emitting–absorbing–scattering media. One of the walls of the enclosure is hot, while the others are cold. The results demonstrate that the bounded skew high-order schemes are more accurate than the bounded high-order ones, regardless of the radiative properties of the medium. The improved accuracy is more significant for the radiation intensity along directions oblique to the coordinate lines, but it is also observed for the incident radiation. The difference between the results of the skewed and the standard schemes is attenuated as the optical thickness of the medium increases. A drawback of the skewed schemes is their higher computational requirements, associated with an increased number of iterations required for convergence.