Bounded, high-resolution differencing schemes applied to the discrete ordinates method

This paper presents an improved spatial differencing practice for the discrete ordinates form of the radiative transport equation (RTE). Several bounded, high-resolution (HR) schemes are applied to the primitive variable form of the RTE in a finite volume context. These schemes provide high accuracy while removing nonphysical oscillations that are characteristic of the diamond difference scheme. A defect correction technique is applied to solve the equations that result from the high-order operators. Predictions from the HR schemes are compared to those of the conventional step and diamond difference schemes for a number of two-dimensional enclosures with gray walls, and either absorbing or isotropically scattering media. Accuracy, stability, and effects on convergence are addressed for the different schemes. The HR schemes were found to provide both accuracy and boundedness at modest computational costs.