Chapter 17 - The Method of Discrete Ordinates (SN-Approximation)

Abstract

Like the spherical harmonics method, the discrete ordinate method is a tool to transform the equation of transfer (for a gray medium, or on a spectral basis) into a set of simultaneous partial differential equations. Like the P N -method, the discrete ordinates or S N -method may be carried out to any arbitrary order and accuracy, although the mathematical formulation of high-order S N -schemes is considerably less involved. First proposed by Chandrasekhar [1] in his work on stellar and atmospheric radiation, the S N -method originally received little attention in the heat transfer community. Again like the P N -method, the discrete ordinates method was first systematically applied to problems in neutron transport theory, notably by Lee [2] and Lathrop [3, 4]. There were some early, unoptimized attempts to apply the method to onedimensional, planar thermal radiation problems (Love et al . [5, 6], Hottel et al . [7], Roux and Smith [8, 9]). But only during the past thirty years has the discrete ordinates method been applied to, and optimized for, general radiative heat transfer problems, primarily through the pioneering works of Fiveland [10–13] and Truelove [14–16].