A Consistent Interpolation Function for the Solution of Radiative Transfer on Triangular Meshes. I—Comprehensive Formulation

Abstract

This article presents a first-order skewed upwinding procedure for application to discretization numerical methods in the context of radiative transfer involving gray participating media. This scheme: (1) yields fast convergence of the algorithm; (2) inherently precludes the possibility of computing negative coefficients to the discretized algebraic equations; (3) reduces false scattering (diffusion); (4) is relatively insensitive to grid orientation; and (5) produces solutions completely free from undesirable oscillations. Theses attributes render the scheme attractive, especially in the context of combined modes of heat transfer and fluid flow problems for which computational time is a major concern. The suggested scheme has been validated by application to several basic test problems discussed in a companion article.

The authors gratefully acknowledge Rodolphe Vaillon (CNRS researcher, CETHIL, INSA de Lyon), Guillaume Gautier (Eng, PSA Group), and Mathieu Francoeur (Researcher, University of Kentucky) for their participation, collaboration, and/or comments during these research works. The authors are also grateful to the Natural Sciences and Engineering Research Council of Canada (NSERC). Thanks go to Alan Wright for helping in the preparation of this manuscript.