Discrete Transfer and Finite Volume Methods for Highly Anisotropically Scattering in Radiative Heat Analysis

Abstract

The present work deals with the performance assessment of the finite volume method (FVM) and discrete transfer method (DTM) in term of their abilities to accurately satisfy conservation of both scattered energy and asymmetry factor of the scattering phase function, after angular discretization and their computational time to calculate the scattering phase function, in radiative transfer problems. Studies are carried out for many representative benchmark problems dealing with one-dimensional steady state radiative heat transfer through participating gray media under diffuse incident irradiation. For problems considered, tests were performed for a wide range of optical thickness, angular resolution, and anisotropic scattering phase function approximation. The results from both DTM and FVM formulations are presented and compared with available analytical and numerical literature solutions. While the two methods were found to give practically the same results, the DTM was found to be much computationally economical than the FVM, to evaluate the scattering phase function.

Keywords:

• Radiative transfer
• transport theory
• numerical method
• discrete transfer method
• finite volume method
• diffuse incidence
• anisotropically scattering phase function