EVALUATION OF DISCRETIZATION ERRORS IN FINITE-VOLUME RADIANT HEAT TRANSFER PREDICTIONS

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Abstract
The application of the finite-volume method to problems of gray, participating-medium radiation heat transfer requires that space be discretized into volumes and direction into solid angles. The radiation transfer equation is replaced by a set of algebraic equations, one for each combination of volume and solid angle. The solution of these equations, which provides the radiation heat transfer, is subject to error as a result of both the spatial and directional discretization. The errors that arise from spatial discretization are well documented, but those that arise from the directional discretization have received little attention and are poorly understood. The present study shows that errors arising from directional discretization cause the radiant heat flux transport within a solid angle to be concentrated along the direction of its centerline. Spatial discretization often results in an artificial spreading of the radiation, so errors due to directional and spatial discretization tend to cancel. There is an additional source of directional discretization error when control-volume boundaries bisect solid angles. This study evaluates the size of this error, and proposes methods of reducing it.

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