A new differencing scheme for the discrete-ordinates method in complex geometries

This paper is an assessment of a new discrete-ordinates algorithm recently developed by the authors for the numerical treatment of radiative participating media in both two- and three-dimensional enclosures. The algorithm is based on the utilization of general characteristic relations instead of the traditional differencing schemes for the spatial marching procedure. It is ideally suited for the treatment of complex geometries, the grid being formed from triangles (2D) or tetrahedra (3D). The method is exempt of any numerical oscillation and may be readily interfaced with the finite-element method for the solution of problems involving other modes of heat transfer. The mathematical derivation is detailed in the text and several examples are given for complex enclosures. The method proves to be very accurate and of good flexibility.