EXAMINATION OF CONVENTIONAL AND EVEN-PARITY FORMULATIONS OF DISCRETE ORDINATES METHOD IN A BODY-FITTED COORDINATE SYSTEM

Abstract

The conventional radiative transfer equation (RTE) and the even-parity formulation (EPF) of the RTE in a general body-fitted coordinate system have been developed and they are used to simulate multi-dimensional radiative heat transfer in irregular geometries by the discrete ordinates method (DOM). The discrete ordinates equations for the EPF are second-order differential equations and they are spatially discretized using a second-order central difference scheme. At the boundary, a higher-order upwind scheme is employed to prevent solution instability and minimize errors. The spatially discretized equations are solved by a preconditioned conjugate gradients method. To investigate the accuracy and efficiency of the conventional RTE and the even-parity RTE in a body-fitted coordinate system, five two-dimensional and three-dimensional benchmark problems with absorbing-emitting and scattering media enclosed by irregular walls are considered. Compared to the conventional RTE, the EPF of the DOM is found to be more sensitive to the grid layout and it requires a clustered grid near the wall in order to provide accurate results in radiative wall heat flux. With an appropriate selection of a grid, the even-parity solution generally has an accuracy close to the conventional discrete ordinates solution. However, it usually requires more CPU time and iterations to converge, especially for the case with a small optical thickness. The present study indicates that the conventional RTE of the DOM is a more computationally robust radiation model than the EPF of the DOM in a body-fitted coordinate system.