Coupled ordinates method for multigrid acceleration of radiation calculations

The finite volume and discrete ordinates methods are known to converge incr easingly slowly as the optical thickness is increased. This is a result of the sequential nature of the solution procedure; the equations for energy a nd the directional intensities are solved one by one, assuming prevailing v alues for other variables. The coupled ordinates method is proposed whereby the discrete energy and intensity equations at each cell are solved simult aneously assuming spatial neighbors to be known. The point-coupled procedur e is used as a relaxation sweep in a multigrid scheme. The formulation of c oarse-level discrete equations admits arbitrary nonconvex polyhedra, making the scheme suitable for use with arbitrary unstructured polyhedral meshes. The scheme is shown to substantially accelerate convergence over a range o f optical thicknesses.