A Skew Upwinding Scheme for Numerical Radiative Transfer

Abstract

This paper exhaustively presents a skewed upwinding procedure for application to finite volume methods (FVMs), finite element methods (FEMs) or control volume finite element methods (CVFEMs) in the context of radiative heat transfer problems involving participating media. The proposed scheme is based on the application of sound physical arguments. Through its basis of development, 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 renders the scheme attractive, especially in the context of combined modes of heat transfer and fluid flow problems for which CPU time is a major concern. The suggested first-order skew upwind (SU) scheme has been validated by application to several basic two-dimensional test problems, acknowledged by the radiative heat transfer community: its performance has proven to be excellent. However, the validation is discussed for a few problems only to avoid making this contribution overly lengthy.