TRANSPORT-DIFFUSION INTERFACES IN RADIATIVE-TRANSFER

For radiative transfer problems involving both optically thick and thin regions, it is suggested that a coupled diffusion-transport treatment has certain advantages in numerical treatments. The well known Marshak (Milne) boundary treatment is extended in a straight-forward way to give the connecting conditions at the diffusion-transport interface. It is found that these conditions give a diffusion radiative flux from a blackbody in excess of the physical blackbody limit. The Marshak conditions are modified to correct this discrepancy and the resulting diffusion description is found to be quite accurate for grey, as well as black, bodies. A previously suggested diffusion-transport interface treatment, due to Brockway, is discussed and shown to be a certain finite difference analogue of the unmodified Marshak treatment. The modification needed to give the correct black-body limit is applied to the Brockway formulation. The previously suggested interpretation of the Brockway equations in terms of probabilities leads to conceptual difficulties, and it is shown that such an interpretation is not needed to successfully apply these interface conditions. © 1979.