COMPARISON OF DISCRETE ORDINATES FORMULATIONS FOR RADIATIVE HEAT-TRANSFER IN MULTIDIMENSIONAL GEOMETRIES

This article compares predictions of radiative heat transfer in two-di mensional enclosures for several formulations of the discrete ordinate s method. The discrete ordinates equations are formulated for an absor bing, isotropically scattering, and re-emitting medium enclosed by gra y walls. Control volume based finite element formulations of the radia tive transport equation (RTE) are presented for the primitive variable (PV) and even parity (EP) equations. These formulations are compared to the finite element formulation of the EP equations, to the control volume formulation of the PV radiative transport equation, and to exac t solutions, Several test enclosures are modeled, including enclosures with either absorbing or isotropically scattering media. Solution acc uracy is investigated for two angular discretization schemes: 1) the S -n discrete ordinates approximation and 2) the piecewise constant angu lar approximation. The PV formulations of the RTE appear to be more ac curate than EP formulations.