Acceleration of Anisotropic Scattering Computations Using Coupled Ordinates Method (COMET)

Traditional sequential solution procedures for solving coupled heat transfer and radiation problems are known to perform very poorly when the optical thickness is high. This poor performance can be traced to the fact that sequential procedures cannot handle strong inter-equation coupling resulting from large absorption and scattering coefficients. This paper extends the use of the coupled ordinates method (COMET) to problems involving anisotropic scattering, where inter-equation coupling results from the in-scattering terms. A finite volume formulation for arbitrary unstructured meshes is used to discretize the radiative transfer equation. An efficient point-solution procedure is devised which is suitable for different scattering phase functions, and eliminates the cubic dependence of the operation count on the angular discretization. This solution scheme is used as a relaxation sweep in a multigrid procedure designed to eliminate long-wavelength errors. The method is applied to scattering problems and shown to substantially accelerate convergence for moderate to large optical thicknesses.